-
question_answer1)
In figure, the graph of a polynomial \[p(x)\] is shown. Find the number of zeroes of \[p(x)\]. |
|
A)
4 done
clear
B)
1 done
clear
C)
2 done
clear
D)
3 done
clear
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question_answer2)
In the figure, graph of a polynomial \[p(x)\] is given. Find the zeroes of\[p(x)\]. |
|
A)
\[-3, 4\] done
clear
B)
\[3, 5\] done
clear
C)
\[-3, 5\] done
clear
D)
\[3, 4\] done
clear
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question_answer3)
The number of zeroes of the polynomial as shown in the graph are: |
|
A)
3 done
clear
B)
4 done
clear
C)
1 done
clear
D)
2 done
clear
View Solution play_arrow
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question_answer4)
In the given figure, the number of zeroes of the polynomial \[f(x)\] are: |
|
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
View Solution play_arrow
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question_answer5)
The number of zeroes lying between \[-4\] and 4 of the polynomial \[f(x)\] whose graph is given below, is: |
|
A)
2 done
clear
B)
3 done
clear
C)
4 done
clear
D)
1 done
clear
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question_answer6)
Which of the following figure represents the graph of a linear polynomial?
A)
B)
C)
D)
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question_answer7)
The given figure shows the graph of the polynomial \[f(x)=a{{x}^{2}}+bx+c,\] then: |
|
A)
\[a>0,\,\,b<0\] and \[c>0\] done
clear
B)
\[a<0,\,\,b<0\] and \[c>0\] done
clear
C)
\[a<0,\,\,\,b>0\]and \[c>0\] done
clear
D)
\[a<0,\,\,b>0\]and \[c<0\] done
clear
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question_answer8)
Which of the following is not the graph of a quadratic polynomial? (NCERT EXEMPLAR)
A)
B)
C)
D)
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question_answer9)
Graph of a quadratic polynomial is a:
A)
straight line done
clear
B)
circle done
clear
C)
parabola done
clear
D)
ellipse done
clear
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question_answer10)
Zeroes of a polynomial can be determined graphically. Number of zeroes of a polynomial is equal to number of points where the graph of polynomial:
A)
intersects Y-axis done
clear
B)
intersects X-axis done
clear
C)
intersects Y-axis or intersects X-axis done
clear
D)
None of the above done
clear
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question_answer11)
If graph of a polynomial does not intersects the X-axis but intersects Y-axis in one point, then number of zeroes of the polynomial is equal to:
A)
0 done
clear
B)
1 done
clear
C)
0 or 1 done
clear
D)
None of these done
clear
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question_answer12)
A polynomial of degree n has:
A)
only 1 zero done
clear
B)
exactly n zeroes done
clear
C)
at most n zeroes done
clear
D)
more than n zeroes done
clear
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question_answer13)
The maximum number of zeroes a cubic polynomial can have, is: (CBSE 2020)
A)
1 done
clear
B)
4 done
clear
C)
2 done
clear
D)
3 done
clear
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question_answer14)
The graph of a quadratic polynomial intersects the X-axis at most at:
A)
1 point done
clear
B)
2 points done
clear
C)
3 points done
clear
D)
0 point done
clear
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question_answer15)
The parabola representing a quadratic polynomial \[f(x)=a{{x}^{2}}+bx+c\]opens upward when:
A)
\[a>0\] done
clear
B)
\[a<0\] done
clear
C)
\[a=0\] done
clear
D)
\[a>0\] done
clear
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question_answer16)
The parabola representing a quadratic polynomial \[f(x)=a{{x}^{2}}+bx+c\]opens downward when:
A)
\[a<0\] done
clear
B)
\[a>0\] done
clear
C)
\[a<1\] done
clear
D)
\[a>1\] done
clear
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question_answer17)
The maximum number of zeroes which a quadratic polynomial can have is:
A)
one done
clear
B)
two done
clear
C)
three done
clear
D)
None of these done
clear
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question_answer18)
If the parabola represented by \[f(x)=a{{x}^{2}}+bx+c\] cuts X-axis at two distinct points, then the polynomial \[a{{x}^{2}}+bx+c\] has .......... real zeroes.
A)
two done
clear
B)
three done
clear
C)
four done
clear
D)
None of these done
clear
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question_answer19)
Find the zeroes of the quadratic polynomial \[{{y}^{2}}-3y+2\].
A)
\[1,-2\] done
clear
B)
\[\frac{-1}{4},\frac{3}{2}\] done
clear
C)
\[6,-1\] done
clear
D)
\[1,2\] done
clear
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question_answer20)
The zeroes of the quadratic polynomial \[{{x}^{2}}+25x+156\]are:
A)
both positive done
clear
B)
both negative done
clear
C)
one positive and one negative done
clear
D)
can't be determined done
clear
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question_answer21)
If one root of the polynomial \[f(x)=3{{x}^{2}}+11x+p\] is reciprocal of the other, then the value p is:
A)
0 done
clear
B)
3 done
clear
C)
1 done
clear
D)
-3 done
clear
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question_answer22)
If the sum of the zeroes of the quadratic polynomial \[k{{x}^{2}}+4x+3k\] is equal to their product, then the value of k is:
A)
\[-\frac{3}{4}\] done
clear
B)
\[\frac{3}{4}\] done
clear
C)
\[\frac{4}{3}\] done
clear
D)
\[-\frac{4}{3}\] done
clear
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question_answer23)
The zeroes of the quadratic polynomial \[{{x}^{2}}+kx+k,\]where \[\text{k}>0\]:
A)
are both positive done
clear
B)
are both negative done
clear
C)
are always equal done
clear
D)
are always unequal done
clear
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question_answer24)
If two zeroes of the polynomial \[{{x}^{3}}+{{x}^{2}}-9x-9\] are 3 and \[-3,\] then its third zero is:
A)
-1 done
clear
B)
1 done
clear
C)
-9 done
clear
D)
9 done
clear
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question_answer25)
If \[\alpha ,\beta ,\gamma \] be the zeroes of the polynomial \[p(x)\] such that \[(\alpha +\beta +\gamma )=3,\] \[(\alpha \beta +\beta \gamma +\gamma \alpha )=-10\] and \[\alpha \beta \gamma =24,\] then \[p(x)=\]
A)
\[{{x}^{3}}+3{{x}^{2}}-10x+24\] done
clear
B)
\[{{x}^{3}}-3{{x}^{2}}-10x-24\] done
clear
C)
\[{{x}^{3}}-3{{x}^{2}}-10x+24\] done
clear
D)
\[None\,\, of\,\, these\] done
clear
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question_answer26)
If \[\alpha ,\beta \] are the zeroes of \[f(x)=2{{x}^{2}}+8x-8,\] then:
A)
\[\alpha +\beta =\alpha \beta \] done
clear
B)
\[\alpha +\beta >\alpha \beta \] done
clear
C)
\[\alpha +\beta <\alpha \beta \] done
clear
D)
\[\alpha +\beta +\alpha \beta =0\] done
clear
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question_answer27)
If the zeroes of the polynomial \[{{x}^{3}}-3{{x}^{2}}+x+1\]are \[\frac{a}{r},\] a and or, then the value of a is:
A)
1 done
clear
B)
-1 done
clear
C)
2 done
clear
D)
-3 done
clear
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question_answer28)
The product of zeroes of the polynomial \[d{{x}^{3}}+c{{x}^{2}}+bx+a\] is:
A)
\[\frac{d}{a}\] done
clear
B)
\[\frac{a}{d}\] done
clear
C)
\[-\frac{d}{a}\] done
clear
D)
\[-\frac{a}{d}\] done
clear
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question_answer29)
If the sum of the zeroes of the polynomial \[f(x)=2{{x}^{3}}-3k{{x}^{2}}+4x-5\] is 6, then the value of k is:
A)
5 done
clear
B)
4 done
clear
C)
-2 done
clear
D)
-4 done
clear
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question_answer30)
The sum and product of zeroes of a quadratic polynomial are \[0\] and \[\sqrt{3}\] respectively. The quadratic polynomial is:
A)
\[{{x}^{2}}-\sqrt{3}\] done
clear
B)
(b)\[{{x}^{2}}+\sqrt{3}\] done
clear
C)
\[{{x}^{2}}-3\] done
clear
D)
\[{{x}^{2}}+3\] done
clear
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question_answer31)
If two zeroes of \[{{x}^{3}}+{{x}^{2}}-3x-3\]are \[\sqrt{3}\] and \[-\sqrt{3},\] then its third zero is:
A)
1 done
clear
B)
-1 done
clear
C)
2 done
clear
D)
-2 done
clear
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question_answer32)
If two of the zeroes of the cubic polynomial \[a{{x}^{3}}+b{{x}^{2}}+cx+d\] are each equal to zero, then the third zero is:
A)
\[-\frac{d}{a}\] done
clear
B)
\[\frac{c}{a}\] done
clear
C)
\[-\frac{b}{a}\] done
clear
D)
\[\frac{b}{a}\] done
clear
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question_answer33)
If the sum of the zeroes of the polynomial \[p(x)=({{p}^{2}}-23){{x}^{2}}-2x-12\] is 1, then p takes the value(s):
A)
\[\sqrt{23}\] done
clear
B)
\[-23\] done
clear
C)
\[2\] done
clear
D)
\[\pm 5\] done
clear
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question_answer34)
If \[\alpha \] and \[\beta \] are the zeroes of the quadratic polynomial \[f(t)={{t}^{2}}-4t+3,\] then the value of \[{{\alpha }^{4}}{{\beta }^{3}}+{{\alpha }^{3}}{{\beta }^{4}}\] is:
A)
104 done
clear
B)
108 done
clear
C)
122 done
clear
D)
5 done
clear
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question_answer35)
The zeroes of the polynomial \[{{x}^{3}}-x\] are:
A)
\[0,\pm 2\] done
clear
B)
\[0,\pm 1\] done
clear
C)
\[0,\pm 3\] done
clear
D)
\[0,\pm 4\] done
clear
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question_answer36)
If \[\alpha ,\beta ,\gamma \] are the zeroes of the polynomial \[{{x}^{3}}+p{{x}^{2}}+qx+r,\] then \[\left( \frac{1}{\alpha \beta }+\frac{1}{\beta \gamma }+\frac{1}{\gamma \alpha } \right)=\]
A)
\[\frac{p}{r}\] done
clear
B)
\[-\frac{p}{r}\] done
clear
C)
\[\frac{q}{r}\] done
clear
D)
\[-\frac{q}{r}\] done
clear
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question_answer37)
If one of the zeroes of the quadratic polynomial \[b{{x}^{2}}+cx+d\] is 0, then the other zero is:
A)
\[-\frac{b}{d}\] done
clear
B)
\[-\frac{c}{b}\] done
clear
C)
\[\frac{b}{d}\] done
clear
D)
\[\frac{c}{b}\] done
clear
View Solution play_arrow
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question_answer38)
The zeroes of polynomial \[{{x}^{2}}-5x+6\] are:
A)
\[-1,0\] done
clear
B)
\[4,5\] done
clear
C)
\[3,2\] done
clear
D)
None of these done
clear
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question_answer39)
If the sum of the zeroes of a polynomial is \[-\frac{1}{6}\]and product of the zeroes of the polynomial is \[-2,\] then the polynomial is:
A)
\[{{x}^{2}}-\frac{1}{6}x+2\] done
clear
B)
\[{{x}^{2}}+\frac{1}{6}x-2\] done
clear
C)
\[6{{x}^{2}}-x+12\] done
clear
D)
\[6{{x}^{2}}+x-12\] done
clear
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question_answer40)
If the product of two zeroes of the polynomial \[f(x)=2{{x}^{3}}+6{{x}^{2}}-4x+7\] is 7, then its third zero is:
A)
\[\frac{1}{2}\] done
clear
B)
\[-\frac{1}{2}\] done
clear
C)
\[\frac{7}{2}\] done
clear
D)
\[-\frac{7}{2}\] done
clear
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question_answer41)
If \[\alpha ,\beta \] are the zeroes of the polynomial \[{{x}^{2}}+5x+c,\] and \[\alpha -\beta =3,\] then c =
A)
0 done
clear
B)
1 done
clear
C)
4 done
clear
D)
5 done
clear
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question_answer42)
If \[\alpha ,\beta \] are the zeroes of the polynomial \[p(x)={{x}^{2}}-2x-3,\]then \[\frac{1}{\alpha }+\frac{1}{\beta }\] is:
A)
\[\frac{2}{3}\] done
clear
B)
\[\frac{1}{3}\] done
clear
C)
\[\frac{-1}{3}\] done
clear
D)
\[-\frac{2}{3}\] done
clear
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question_answer43)
For what value of p, 1 is a zero of the polynomial \[f(x)=2{{x}^{2}}+5x-(3p+1)\]?
A)
\[3\] done
clear
B)
\[5\] done
clear
C)
\[2\] done
clear
D)
\[-1\] done
clear
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question_answer44)
If \[\alpha ,\beta \] are the zeroes of the polynomial \[f(x)={{x}^{2}}-p(x+1)-q,\] then \[(\alpha +1)\,\,(\beta +1)=\]
A)
\[q-1\] done
clear
B)
\[1-q\] done
clear
C)
\[q\] done
clear
D)
\[1+q\] done
clear
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question_answer45)
A quadratic polynomial, the sum of whose zeroes is 0 and one zero is 4, is:
A)
\[{{x}^{2}}-16\] done
clear
B)
\[{{x}^{2}}+16\] done
clear
C)
\[{{x}^{2}}+4\] done
clear
D)
\[{{x}^{2}}-4\] done
clear
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question_answer46)
If the zeroes of the quadratic polynomial \[{{x}^{2}}+(a+1)x+b\] are \[4\] and \[-3,\] then \[a-b\] is:
A)
12 done
clear
B)
\[10\] done
clear
C)
\[7\] done
clear
D)
\[1\] done
clear
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question_answer47)
If \[\alpha \] and \[\beta \] be the zeroes of the polynomial \[p(x)={{x}^{2}}-5x+2,\] find the value of \[\frac{1}{\alpha }+\frac{1}{\beta }-3\alpha \beta \].
A)
\[-\frac{3}{2}\] done
clear
B)
\[-\frac{5}{2}\] done
clear
C)
\[-\frac{7}{2}\] done
clear
D)
\[-\frac{9}{2}\] done
clear
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question_answer48)
If \[\alpha ,\beta ,\gamma \] are the zeroes of the polynomial \[f(x)={{x}^{3}}-a{{x}^{2}}+bx-c,\]then\[\frac{1}{\alpha \beta }+\frac{1}{\beta \gamma }+\frac{1}{\gamma \alpha }=\]
A)
\[\frac{c}{a}\] done
clear
B)
\[\frac{a}{c}\] done
clear
C)
\[-\frac{a}{c}\] done
clear
D)
\[-\frac{c}{a}\] done
clear
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question_answer49)
The zeroes of the polynomial \[f(x)={{x}^{2}}-2\sqrt{2}x-16\] are:
A)
\[\sqrt{2},-\sqrt{2}\] done
clear
B)
\[4\sqrt{2},-2\sqrt{2}\] done
clear
C)
\[-4\sqrt{2},2\sqrt{2}\] done
clear
D)
\[4\sqrt{2},2\sqrt{2}\] done
clear
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question_answer50)
If \[\alpha ,\beta ,\gamma \] are zeroes of the polynomial \[f(x)={{x}^{3}}-3p{{x}^{2}}+qx-r\] such that \[2\beta =\alpha +\gamma \] then:
A)
\[2{{p}^{3}}=pq-r\] done
clear
B)
\[2{{p}^{3}}=pq+r\] done
clear
C)
\[{{p}^{3}}=pq-r\] done
clear
D)
None of these done
clear
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question_answer51)
If \[\alpha ,\beta ,\gamma \] are the zeroes of the polynomial \[f(x)=a{{x}^{3}}+b{{x}^{2}}+cx+d,\] then \[\frac{1}{\alpha }+\frac{1}{\beta }+\frac{1}{\gamma }=\]
A)
\[-\frac{b}{a}\] done
clear
B)
\[\frac{c}{d}\] done
clear
C)
\[-\frac{c}{d}\] done
clear
D)
\[-\frac{c}{a}\] done
clear
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question_answer52)
The zeroes of the polynomial \[f(x)={{x}^{2}}+x-\frac{3}{4}\] are:
A)
\[-\frac{1}{2},\frac{3}{2}\] done
clear
B)
\[\frac{1}{2},-\frac{3}{2}\] done
clear
C)
\[1,-\frac{3}{2}\] done
clear
D)
\[1,\frac{\sqrt{3}}{2}\] done
clear
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question_answer53)
If a, p are zeroes of the polynomial \[f(x)=a{{x}^{2}}+bx+c,\]then \[\frac{1}{{{\alpha }^{2}}}+\frac{1}{{{\beta }^{2}}}=\]
A)
\[\frac{{{b}^{2}}-2ac}{{{a}^{2}}}\] done
clear
B)
\[\frac{{{b}^{2}}-2ac}{{{c}^{2}}}\] done
clear
C)
\[\frac{{{b}^{2}}+2ac}{{{a}^{2}}}\] done
clear
D)
\[\frac{{{b}^{2}}+2ac}{{{c}^{2}}}\] done
clear
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question_answer54)
If one of the zeroes of the quadratic polynomial \[(k-1){{x}^{2}}+kx+1\] is \[-3,\] then the value of k is: (NCERT EXEMPLAR)
A)
\[\frac{4}{3}\] done
clear
B)
\[\frac{-4}{3}\] done
clear
C)
\[\frac{2}{3}\] done
clear
D)
\[\frac{-2}{3}\] done
clear
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question_answer55)
A quadratic polynomial, whose zeroes are \[-3\] and 4, is: (NCERT EXEMPLAR)
A)
\[{{x}^{2}}-x+12\] done
clear
B)
\[{{x}^{2}}+x+12\] done
clear
C)
\[\frac{{{x}^{2}}}{2}-\frac{x}{2}-6\] done
clear
D)
\[2{{x}^{2}}+2x-24\] done
clear
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question_answer56)
If the zeroes of the quadratic polynomial \[{{x}^{2}}+(a+1)x+b\] are \[2\] and \[-3,\] then: (NCERT EXEMPLAR)
A)
\[a=-7,\,\,b=-1\] done
clear
B)
\[a=5,\,\,b=-1\] done
clear
C)
\[a=2,\,b=-6\] done
clear
D)
\[a=0,\,b=-6\] done
clear
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question_answer57)
The number of polynomials having zeroes as \[-2\] and 5 is: (NCERT EXEMPLAR)
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
more than 3 done
clear
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question_answer58)
Given that one of the zeroes of the cubic polynomial \[a{{x}^{3}}+b{{x}^{2}}+cx+d\] is zero, the product of the other two zeroes is: (NCERT EXEMPLAR)
A)
\[-\frac{c}{a}\] done
clear
B)
\[\frac{c}{a}\] done
clear
C)
\[0\] done
clear
D)
\[-\frac{b}{a}\] done
clear
View Solution play_arrow
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question_answer59)
If one of the zeroes of the cubic polynomial \[{{x}^{3}}+a{{x}^{2}}+bx+c\] is \[-1,\] then the product of the other two zeroes is: (NCERT EXEMPLAR)
A)
\[b-a+1\] done
clear
B)
\[b-a-1\] done
clear
C)
\[a-b+1\] done
clear
D)
\[a-b-1\] done
clear
View Solution play_arrow
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question_answer60)
The zeroes of the quadratic polynomial \[{{x}^{2}}+99x+127\] are: (NCERT EXEMPLAR)
A)
both positive done
clear
B)
both negative done
clear
C)
one positive and one negative done
clear
D)
both equal done
clear
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question_answer61)
The zeroes of the quadratic polynomial \[{{x}^{2}}+kx+k,\] \[k\ne 0\]: (NCERT EXEMPLAR)
A)
cannot both be positive done
clear
B)
cannot both be negative done
clear
C)
are always unequal done
clear
D)
are always equal done
clear
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question_answer62)
If the zeroes of the quadratic polynomial \[a{{x}^{2}}+bx+c,\] \[c\ne 0\]are equal. then: (NCERT EXEMPLAR)
A)
c and a have opposite signs done
clear
B)
c and b have opposite signs done
clear
C)
c and a have the same sign done
clear
D)
c and b have the same sign done
clear
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question_answer63)
If one of the zeroes of a quadratic polynomial of the form \[{{x}^{2}}+ax+b\] is the negative of the other, then it: (NCERT EXEMPLAR)
A)
has no linear term and the constant term is negative done
clear
B)
has no linear term and the constant term is positive done
clear
C)
can have a linear term but the constant term is negative done
clear
D)
can have a linear term but the constant term is positive done
clear
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question_answer64)
The quadratic polynomial whose sum of zeroes is 3 and product of zeroes is \[-2\] is: (CBSE 2011)
A)
\[{{x}^{2}}+3x-2\] done
clear
B)
\[{{x}^{2}}-2x+3\] done
clear
C)
\[{{x}^{2}}-3x+2\] done
clear
D)
\[{{x}^{2}}-3x-2\] done
clear
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question_answer65)
If \[(x+1)\] is a factor of \[2{{x}^{3}}+a{{x}^{2}}+2bx+1,\] then find the values of a and b given that \[2a-3b=4\]: (CBSE 2011)
A)
\[a=-1,\,b=-2\] done
clear
B)
\[a=2,\,b=5\] done
clear
C)
\[a=5,\,b=2\] done
clear
D)
\[a=2,\,b=0\] done
clear
View Solution play_arrow
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question_answer66)
The number of zeroes that polynomial \[f(x)={{(x-2)}^{2}}+4\] can have is: (CBSE 2012)
A)
1 done
clear
B)
2 done
clear
C)
0 done
clear
D)
3 done
clear
View Solution play_arrow
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question_answer67)
The zeroes of the polynomial \[f(x)=4{{x}^{2}}-12x+9\] are: (CBSE 2012)
A)
\[\frac{3}{2},\frac{3}{2}\] done
clear
B)
\[-\frac{3}{2},-\frac{3}{2}\] done
clear
C)
\[3,4\] done
clear
D)
\[-3,-4\] done
clear
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question_answer68)
If \[p(x)\] is a polynomial of at least degree one and \[p(k)=0,\]then k is known as:
A)
value of \[p(x)\] done
clear
B)
zero of \[p(x)\] done
clear
C)
constant term of \[p(x)\] done
clear
D)
None of these done
clear
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question_answer69)
If \[p(x)=ax+b,\]then zero of \[p(x)\] is:
A)
\[a\] done
clear
B)
\[b\] done
clear
C)
\[\frac{-a}{b}\] done
clear
D)
\[\frac{-b}{a}\] done
clear
View Solution play_arrow
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question_answer70)
If \[p(x)=a{{x}^{2}}+bx+c,\] then \[\frac{c}{a}\] is equal to:
A)
\[0\] done
clear
B)
\[1\] done
clear
C)
sum of zeroes done
clear
D)
product of zeroes done
clear
View Solution play_arrow
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question_answer71)
If \[p(x)=a{{x}^{2}}+bx+c,\] then \[-\frac{b}{a}\]is equal to:
A)
\[0\] done
clear
B)
\[1\] done
clear
C)
product of zeroes done
clear
D)
sum of zeroes done
clear
View Solution play_arrow
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question_answer72)
If \[p(x)=a{{x}^{2}}+bx+c\]and \[a+b+c=0,\] then one zero is:
A)
\[\frac{-b}{a}\] done
clear
B)
\[\frac{c}{a}\] done
clear
C)
\[\frac{b}{c}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer73)
If \[p(x)=a{{x}^{2}}+bx+c\]and \[\text{a}+\text{c}=\text{b},\] then one of the zeroes is:
A)
\[\frac{b}{a}\] done
clear
B)
\[\frac{c}{a}\] done
clear
C)
\[\frac{-c}{a}\] done
clear
D)
\[\frac{-b}{a}\] done
clear
View Solution play_arrow
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question_answer74)
A quadratic polynomial whose one zero is 6 and sum of the zeroes is 0, is:
A)
\[{{x}^{2}}-6x+2\] done
clear
B)
\[{{x}^{2}}-36\] done
clear
C)
\[{{x}^{2}}-6\] done
clear
D)
\[{{x}^{2}}-3\] done
clear
View Solution play_arrow
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question_answer75)
A quadratic polynomial whose one zero is 5 and product of zeroes is 0, is:
A)
\[{{x}^{2}}-5\] done
clear
B)
\[{{x}^{2}}-5x\] done
clear
C)
\[5{{x}^{2}}+1\] done
clear
D)
\[{{x}^{2}}+5x\] done
clear
View Solution play_arrow
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question_answer76)
For a given value of k, the product of the zeroes of \[{{x}^{2}}-3kx+2{{k}^{2}}-1\] is 7, then zeroes are:
A)
rational numbers done
clear
B)
irrational numbers done
clear
C)
one rational, other irrational done
clear
D)
None of the above done
clear
View Solution play_arrow
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question_answer77)
If zeroes of \[p(x)=2{{x}^{2}}-7x+k\] are reciprocal of each other, then value of k is:
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
\[-7\] done
clear
View Solution play_arrow
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question_answer78)
Zeroes of \[p(z)={{z}^{2}}-27\] are:
A)
\[2\sqrt{3},\,\,3\sqrt{3}\] done
clear
B)
\[\,\,3\sqrt{3},\,-3\sqrt{3}\] done
clear
C)
\[\sqrt{3},\,-\sqrt{3}\] done
clear
D)
\[2\sqrt{2},\,-2\sqrt{2}\] done
clear
View Solution play_arrow
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question_answer79)
The zeroes of the quadratic polynomial \[{{x}^{2}}+7x+12\] are:
A)
\[-2,-5\] done
clear
B)
\[-3,-4\] done
clear
C)
\[2,5\] done
clear
D)
\[3,4\] done
clear
View Solution play_arrow
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question_answer80)
The zeroes of the polynomial \[{{x}^{2}}-3x-m(m+3)\] are: (CBSE 2020)
A)
\[m,\,\,m+3\] done
clear
B)
\[-m,\,\,m+3\] done
clear
C)
\[m,-(\,\,m+3)\] done
clear
D)
\[-m,-(\,\,m+3)\] done
clear
View Solution play_arrow
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question_answer81)
Find a quadratic polynomial, the sum and product of whose zeroes are \[-7\] and \[-2\].
A)
\[{{x}^{2}}-7x-2\] done
clear
B)
\[{{x}^{2}}-7x+2\] done
clear
C)
\[{{x}^{2}}+7x-2\] done
clear
D)
\[{{x}^{2}}+2x-7\] done
clear
View Solution play_arrow
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question_answer82)
Find a quadratic polynomial, the sum and product of whose zeroes are \[-\frac{1}{4},\frac{1}{4}\]. (NCERT EXERCISE)
A)
\[4{{x}^{2}}-x+1\] done
clear
B)
\[4{{x}^{2}}+x-1\] done
clear
C)
\[4{{x}^{2}}+x+1\] done
clear
D)
\[None\,\, of\,\, these\] done
clear
View Solution play_arrow
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question_answer83)
If \[\alpha \] and \[\beta \] are the zeroes of the polynomial \[2{{x}^{2}}-13x+6,\] then \[\alpha +\beta \] is: (CBSE 2020)
A)
\[-3\] done
clear
B)
\[3\] done
clear
C)
\[\frac{13}{2}\] done
clear
D)
\[-\frac{13}{2}\] done
clear
View Solution play_arrow
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question_answer84)
If the sum of the zeroes of the quadratic polynomial \[k{{x}^{2}}+2x+3k\] is equal to their product, then k equals: (CBSE 2020)
A)
\[\frac{1}{3}\] done
clear
B)
\[-\frac{1}{3}\] done
clear
C)
\[\frac{2}{3}\] done
clear
D)
\[-\frac{2}{3}\] done
clear
View Solution play_arrow
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question_answer85)
If one zero of the polynomial \[3{{x}^{2}}+8x+k\] is the reciprocal of the other, then value of k is: (CBSE 2020)
A)
\[3\] done
clear
B)
\[-3\] done
clear
C)
\[\frac{1}{3}\] done
clear
D)
\[-\frac{1}{3}\] done
clear
View Solution play_arrow
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question_answer86)
If \[a+b+c=0,\] then a zero of the polynomial \[a{{x}^{2}}+bx+c,\]is:
A)
\[1\] done
clear
B)
\[0\] done
clear
C)
\[-1\] done
clear
D)
\[\frac{1}{2}\] done
clear
View Solution play_arrow
-
question_answer87)
If \[\text{a}+\text{c}=\text{b},\]then a zero of the polynomial \[a{{x}^{2}}+bx+c,\]is:
A)
\[1\] done
clear
B)
\[0\] done
clear
C)
\[-1\] done
clear
D)
\[-\frac{1}{2}\] done
clear
View Solution play_arrow
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question_answer88)
If two of the zeroes of a cubic polynomial are zero, then it does not have:
A)
linear done
clear
B)
quadratic done
clear
C)
cubic done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer89)
If two of the zeroes of a cubic polynomial are zero, then it does not have:
A)
constant term done
clear
B)
term of x done
clear
C)
term of \[{{x}^{2}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer90)
If all the zeroes of a cubic polynomial \[{{x}^{3}}+a{{x}^{2}}-bx+c\]are negative then a, b and c all have:
A)
positive terms done
clear
B)
negative terms done
clear
C)
positive and negative both terms done
clear
D)
None of the above done
clear
View Solution play_arrow
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question_answer91)
If the zeroes of the quadratic polynomial \[a{{x}^{2}}+x+a\] are equal, then value of a is:
A)
\[\frac{1}{2}\] done
clear
B)
\[-\frac{1}{2}\] done
clear
C)
\[\pm \frac{1}{2}\] done
clear
D)
\[\pm 1\] done
clear
View Solution play_arrow
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question_answer92)
If the zeroes of the quadratic polynomial \[a{{x}^{2}}+bx+c\] are both negative, then a, b and c all have the:
A)
same sign done
clear
B)
positive sign done
clear
C)
negative sign done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer93)
If \[a,\,a+b,\,\,a+2ab\] are zeroes of the cubic polynomial \[{{x}^{3}}-6{{x}^{2}}+3x+10,\] then \[a+b\] is equal to:
A)
\[1\] done
clear
B)
\[-1\] done
clear
C)
\[0\] done
clear
D)
\[2\] done
clear
View Solution play_arrow
-
question_answer94)
If one zero of the quadratic polynomial \[\text{2}{{\text{x}}^{2}}-\text{6kx}+\text{6x}-\text{7}\]is negative of the other, then k is equal to:
A)
\[-1\] done
clear
B)
\[1\] done
clear
C)
\[0\] done
clear
D)
\[-\frac{1}{2}\] done
clear
View Solution play_arrow
-
question_answer95)
If the product of the zeroes of the quadratic polynomial \[{{x}^{2}}-3ax+2{{a}^{2}}-1\] is 7, then a is equal to:
A)
\[\pm 1\] done
clear
B)
\[\pm \frac{1}{2}\] done
clear
C)
\[\pm 2\] done
clear
D)
\[\pm 3\] done
clear
View Solution play_arrow
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question_answer96)
The sum of the zeroes of the quadratic polynomial \[2{{x}^{2}}-3k\] is:
A)
\[0\] done
clear
B)
\[1\] done
clear
C)
\[2\] done
clear
D)
\[3\] done
clear
View Solution play_arrow
-
question_answer97)
If \[\alpha \] and \[\beta \] are zeroes and the quadratic polynomial \[f(x)={{x}^{2}}-x-4,\] then the value of \[\frac{1}{\alpha }+\frac{1}{\beta }-\alpha \beta \] is:
A)
\[\frac{15}{4}\] done
clear
B)
\[\frac{-15}{4}\] done
clear
C)
\[4\] done
clear
D)
\[15\] done
clear
View Solution play_arrow
-
question_answer98)
The value of the polynomial \[{{x}^{8}}-{{x}^{5}}+{{x}^{2}}-x+1\] is:
A)
positive for all the real numbers done
clear
B)
negative for all the real numbers done
clear
C)
0 done
clear
D)
depends on value of x done
clear
View Solution play_arrow
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question_answer99)
If \[x=0.\overline{7}\] then \[2x\] is:
A)
\[1.\bar{4}\] done
clear
B)
\[1.\bar{5}\] done
clear
C)
\[1.\overline{54}\] done
clear
D)
\[1.\overline{45}\] done
clear
View Solution play_arrow
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question_answer100)
Lowest value of \[{{x}^{2}}+4x+2\] is:
A)
\[0\] done
clear
B)
\[-2\] done
clear
C)
\[2\] done
clear
D)
\[4\] done
clear
View Solution play_arrow
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question_answer101)
If a quadratic polynomial curve in the shape of semicircle is shown below. |
|
Then, the equation of this curve is: |
A)
\[-{{x}^{2}}+2\] done
clear
B)
\[{{x}^{2}}+2\] done
clear
C)
\[\frac{1}{2}{{x}^{2}}+2\] done
clear
D)
\[-\frac{1}{2}{{x}^{2}}+2\] done
clear
View Solution play_arrow
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question_answer102)
If the sum of the zeroes of the polynomial \[f(x)=2{{x}^{3}}-3k{{x}^{2}}+4x-5\] is 6, then the value of x is:
A)
2 done
clear
B)
-2 done
clear
C)
4 done
clear
D)
-4 done
clear
View Solution play_arrow
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question_answer103)
If a cubic polynomial with the sum of its zeroes, sum of the products and its zeroes taken two at a time and product of its zeroes as \[2,\,\,-5\] and \[-11\] respectively, then the cubic polynomial is:
A)
\[{{x}^{3}}+7x-6\] done
clear
B)
\[{{x}^{3}}+7x+6\] done
clear
C)
\[{{x}^{3}}-7x-6\] done
clear
D)
\[{{x}^{3}}-7x+6\] done
clear
View Solution play_arrow
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question_answer104)
If \[\alpha \]and \[\beta \] are the zeroes of the quadratic polynomial \[f(x)=a{{x}^{2}}+bx+c,\] then the value of \[{{\alpha }^{4}}+{{\beta }^{4}}\] is:
A)
\[\frac{{{({{b}^{2}}-2ac)}^{2}}+{{a}^{2}}{{c}^{2}}}{{{a}^{4}}}\] done
clear
B)
\[\frac{{{({{b}^{2}}+2ac)}^{2}}-{{a}^{2}}{{c}^{2}}}{{{a}^{4}}}\] done
clear
C)
\[\frac{{{({{b}^{2}}-2ac)}^{2}}-2{{a}^{2}}{{c}^{2}}}{{{a}^{4}}}\] done
clear
D)
\[\frac{{{({{b}^{2}}+2ac)}^{2}}+2{{a}^{2}}{{c}^{2}}}{{{a}^{4}}}\] done
clear
View Solution play_arrow
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question_answer105)
If one of the zeroes of a quadratic polynomial of the form \[{{x}^{2}}+ax+b\] is the negative of the other, then which of the following is correct?
A)
Polynomial has linear factors done
clear
B)
Constant term of polynomial is negative done
clear
C)
Both a and b are correct done
clear
D)
Neither a nor b is correct done
clear
View Solution play_arrow
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question_answer106)
If \[\alpha ,\beta \] and \[\gamma \] are the zeroes of the polynomial \[p(x)=a{{x}^{3}}+3b{{x}^{2}}+3cx+d\] and having relation\[2\beta =\alpha +\gamma ,\]then \[2{{b}^{3}}-3abc+{{a}^{2}}d\] is:
A)
-1 done
clear
B)
1 done
clear
C)
0 done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer107)
If the square of difference of the zeroes of the quadratic polynomial \[{{x}^{2}}+px+45\] is equal to 144, then the value of p is:
A)
\[\pm 9\] done
clear
B)
\[\pm 12\] done
clear
C)
\[\pm 15\] done
clear
D)
\[\pm 18\] done
clear
View Solution play_arrow
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question_answer108)
If \[\alpha \] and \[\beta \] are zeroes and the quadratic polynomial \[p(S)=3{{S}^{2}}-6S+4,\] then the value of \[\frac{\alpha }{\beta }+\frac{\beta }{\alpha }+2\left( \frac{1}{\alpha }+\frac{1}{\beta } \right)+3\alpha \beta \]is
A)
7 done
clear
B)
\[6\] done
clear
C)
\[8\] done
clear
D)
\[10\] done
clear
View Solution play_arrow
-
question_answer109)
If the sum of the zeroes of the equation \[\frac{1}{x+a}+\frac{1}{x+b}=\frac{1}{c}\]is zero, then the product of zeroes of the equation is?
A)
\[\frac{{{a}^{2}}+{{b}^{2}}}{2}\] done
clear
B)
\[\frac{-({{a}^{2}}+{{b}^{2}})}{2}\] done
clear
C)
\[\frac{ab}{2}\] done
clear
D)
\[\frac{{{(a+b)}^{2}}}{2}\] done
clear
View Solution play_arrow
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question_answer110)
Draw the graph of the polynomial \[-{{x}^{2}}+x+2\] and find the maximum value of the polynomial.
A)
\[2\] done
clear
B)
\[\frac{5}{2}\] done
clear
C)
\[\frac{9}{4}\] done
clear
D)
\[None\,\, of\,\, these\] done
clear
View Solution play_arrow