question_answer 1)
If the zeroes of the quadratic polynomial \[{{\mathbf{x}}^{\mathbf{2}}}+\left( \mathbf{a}+\mathbf{3} \right)\,\,\mathbf{x}+\mathbf{b}\]are 3 and - 4, then
A)
\[a=2,\text{ }b=6\] done
clear
B)
\[a=-\,2,\text{ }b=-12\] done
clear
C)
\[a=3,\text{ }b=4\] done
clear
D)
\[a=4,\text{ }b=-\,3\] done
clear
E)
None of these done
clear
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question_answer 2)
See the graph given below: (i) (ii) (iii) Based on these graphs, identify the correct statement among the following:
A)
In case ii, the quadratic polynomial \[a\,{{x}^{2}}+\text{ }bx\text{ }+\text{ }c\]has two distinct zeroes. done
clear
B)
In case i, the quadratic polynomial \[a{{x}^{2}}+bx\text{ }+\text{ }c\] has two equal zeroes. done
clear
C)
In case iii, the quadratic polynomial has no zero. done
clear
D)
All the above done
clear
E)
None of these done
clear
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question_answer 3)
Which one among the following statements is incorrect?
A)
Graph of a linear polynomial is a straight line whereas the graph of a quadratic polynomial has one of the two shapes of parabola either open upwards
or open downwards
.
done
clear
B)
The shape of the parabola depends on the value of 'a' of the quadratic polynomial\[a{{x}^{2}}+bx\text{ }+\text{ }c\]. done
clear
C)
The zeroes of a quadratic polynomial \[a{{x}^{2}}+bx\text{ }+\text{ }c\], \[a\ne 0\] are y coordinates of the points where the parabola \[y=a{{x}^{2}}+bx+c\]intersects the y-axis. done
clear
D)
A real number m is a zero of the polynomial p(x) if p (m) = 0 done
clear
E)
None of these done
clear
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question_answer 4)
A polynomial of degree n has ________
A)
two zeroes done
clear
B)
n zeroes done
clear
C)
atleast n zeroes done
clear
D)
atmost n zeroes done
clear
E)
None of these done
clear
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question_answer 5)
If one zero of the quadratic polynomial \[{{x}^{2}}+5x+\text{ }k\]is 3 then second zero of this polynomial is ______
A)
5 done
clear
B)
\[-\]3 done
clear
C)
\[-\]5 done
clear
D)
\[-\]8 done
clear
E)
None of these done
clear
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question_answer 6)
If the zeroes of a quadratic polynomial \[a{{x}^{2}}+bx+c\] are both negative, then
A)
a is positive., b and c are negative done
clear
B)
a is negative/ b and c are positive done
clear
C)
a and c are negative, b is positive done
clear
D)
a, b and c all have the same sign done
clear
E)
None of these done
clear
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question_answer 7)
If \[\mathbf{(3 +}\sqrt{\mathbf{3}}\mathbf{)}\]is one of the zeroes of the quadratic polynomial \[{{\mathbf{x}}^{\mathbf{2}}}+\mathbf{mx}+\mathbf{6}\]then find the second zero.
A)
\[-\sqrt{3}\] done
clear
B)
\[3-\sqrt{3}\] done
clear
C)
3\[+\sqrt{3}\] done
clear
D)
\[\sqrt{3}\] done
clear
E)
None of these done
clear
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question_answer 8)
For a quadratic polynomial \[\mathbf{2}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-8x+b,}\]sum of its roots is 4 and one of the roots is \[\frac{\mathbf{4+}\sqrt{\mathbf{2}}}{\mathbf{2}}\], then the value of b is______
A)
3 done
clear
B)
6 done
clear
C)
7 done
clear
D)
8 done
clear
E)
None of these done
clear
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question_answer 9)
If the zeroes of the quadratic polynomial \[p(x)=ab{{x}^{2}}-({{b}^{2}}-ac)x-\,bc\] are \[\alpha \] & \[\beta \], then
A)
\[\alpha =\frac{-{{b}^{2}}}{a}and\,\beta =\frac{-\,{{c}^{2}}}{b}\] done
clear
B)
\[\alpha =\frac{a}{b}\,\,and\,\beta =\frac{b}{c}\] done
clear
C)
\[\alpha =\frac{b}{a}\,\,and\,\beta =\frac{-\,c}{b}\] done
clear
D)
\[\alpha =\frac{-a}{b}\,\,and\,\,\beta =\frac{c}{b}\] done
clear
E)
None of these done
clear
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question_answer 10)
If \[\alpha \] and \[\beta \] are zeroes of the quadratic polynomial \[p\left( x \right)=a{{x}^{2}}~-\text{ }bx+c,\] then the value of \[\frac{\alpha }{\beta }+\frac{\beta }{\alpha }\] is _________.
A)
\[\frac{{{b}^{2}}+ac}{ac}\] done
clear
B)
\[\frac{{{b}^{2}}-ac}{ac}\] done
clear
C)
\[\frac{{{b}^{2}}+2ac}{ac}\] done
clear
D)
\[\frac{{{c}^{2}}+2ac}{ac}\] done
clear
E)
None of these done
clear
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question_answer 11)
If the zeroes of the quadratic polynomial \[a{{x}^{2}}-x-b\] are \[\frac{-\,3}{2}\] and \[\frac{5}{3}\], then
A)
a = 15, b = 6 done
clear
B)
a = 6, b = 15 done
clear
C)
a = 12, b = 4 done
clear
D)
a = 4, b = 12 done
clear
E)
None of these done
clear
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question_answer 12)
If \[p(x)=25{{x}^{2}}-15x-a\] where \[\alpha \] and \[\beta \] are the zeroes of the polynomial, also if it is given tha \[{{\alpha }^{3}}+{{\beta }^{3}}=\frac{63}{125}\], then
A)
a = 5 done
clear
B)
roots are\[\frac{-1}{5}\]and\[\frac{4}{5}\] done
clear
C)
a = 3 done
clear
D)
roots are \[\frac{1}{5}\] and\[\frac{-2}{5}\] done
clear
E)
None of these done
clear
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question_answer 13)
If two zeroes of the cubic polynomial \[p{{x}^{2}}+q{{x}^{2}}+rx+s\] are 0, then the third zero is _________
A)
\[\frac{p}{q}\] done
clear
B)
\[\frac{-p}{q}\] done
clear
C)
\[-\frac{p}{q}\] done
clear
D)
0 done
clear
E)
None of these done
clear
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question_answer 14)
If one of the zeroes of a cubic polynomial of the form \[{{x}^{3}}+a{{x}^{2}}+bx+c\] is the negative of the other, then
A)
a is of negative sign and b and c are of positive sign done
clear
B)
b is of negative sign and a and c are of positive sign done
clear
C)
a and c are of opposite signs and b is of negative sign done
clear
D)
a and b are of opposite signs and c is of positive sign done
clear
E)
None of these done
clear
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question_answer 15)
If all the zeroes of the cubic polynomial \[{{x}^{3}}+c\,{{x}^{2}}+d\,x+b\] are equal, then
A)
cd = 9 b done
clear
B)
bd = 8 b done
clear
C)
cd = 6 b done
clear
D)
bd = 8 b done
clear
E)
None of these done
clear
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question_answer 16)
If p and q are the of the polynomial \[b{{x}^{2}}+cx+a,\] value of \[\frac{\mathbf{1}}{{{\mathbf{p}}^{\mathbf{3}}}}\mathbf{+}\frac{\mathbf{1}}{{{\mathbf{q}}^{\mathbf{3}}}}\] is ___________
A)
\[\frac{3abc-{{c}^{3}}}{a{{b}^{2}}}\] done
clear
B)
\[\frac{3abc+{{c}^{3}}}{a{{b}^{2}}}\] done
clear
C)
\[\frac{3abc-{{c}^{3}}}{{{a}^{2}}b}\] done
clear
D)
\[\frac{3abc+{{c}^{3}}}{{{a}^{2}}b}\] done
clear
E)
None of these done
clear
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question_answer 17)
If the zeroes of the polynomial\[6{{x}^{2}}+7\sqrt{3}x-15=0\] are \[\alpha \] & \[\beta \], then
A)
\[\alpha =\frac{-\sqrt{3}}{2}\,\,\And \,\,\beta =\frac{5\sqrt{3}}{3}\] done
clear
B)
\[\alpha =-\sqrt{3}\,\,\And \,\,\beta =5\sqrt{3}\] done
clear
C)
\[\alpha =\frac{\sqrt{3}}{2}\,\,\,\And \,\,\beta =\frac{-\,5\sqrt{3}}{3}\] done
clear
D)
\[\alpha =5\sqrt{3}\,\,\And \,\,\beta =-\,\sqrt{3}\] done
clear
E)
None of these done
clear
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question_answer 18)
If \[\alpha \] & \[\beta \] are the zeroes of the quadratic polynomial \[3{{x}^{2}}-11x+6,\] then find the polynomial whose zeroes are \[(2\alpha +\beta )\] and \[(\alpha +2\beta )\]
A)
\[k\,\,\left( {{x}^{2}}-5x+\frac{270}{9} \right)\], \[k\] is any non-zero real number done
clear
B)
\[k\,\,\left( {{x}^{2}}-11x+\frac{260}{9} \right)\], \[k\] is any non-zero real number done
clear
C)
\[k\,(3{{x}^{2}}-3x+26),\] \[k\] is any non-zero real number done
clear
D)
\[k\,(2{{x}^{2}}-5x+27),\] \[k\] is any non-zero real number done
clear
E)
None of these done
clear
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question_answer 19)
If \[\alpha,\beta \] & \[\gamma \] are the roots of the equation \[{{x}^{3}}-4{{x}^{2}}-53x+168\] then the relation between their roots is _______
A)
\[3\alpha +\beta =2\,\gamma \] done
clear
B)
\[3\alpha +4\beta =4\,\gamma \] done
clear
C)
\[3\alpha +\beta =4\,\gamma \] done
clear
D)
\[\alpha +2\beta =\,\gamma \] done
clear
E)
None of these done
clear
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question_answer 20)
What must be subtracted from \[6{{x}^{4}}+16{{x}^{3}}+15{{x}^{2}}-8x+9,\] so that it is exactly divisible by\[3{{x}^{2}}+5x-2\]?
A)
\[-19x+15\] done
clear
B)
\[19x+16\] done
clear
C)
\[13x+19\] done
clear
D)
\[19x-15\] done
clear
E)
None of these done
clear
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question_answer 21)
If \[p(x)={{x}^{3}}-10{{x}^{2}}+31x-30\] and \[q(x)={{x}^{3}}-12{{x}^{2}}+41x-42\], then find the LCM of the polynomials p(x) and q(x).
A)
\[{{x}^{4}}-\text{ }17{{x}^{3}}+\text{ }101{{x}^{2}}-\text{ }247x\text{ }+\text{ }210\] done
clear
B)
\[{{x}^{3}}-\text{ }36{{x}^{2}}+\text{ }90x\text{ }+\text{ }105\] done
clear
C)
\[{{x}^{4}}+\text{ }18{{x}^{3}}-\text{ }95{{x}^{2}}+\text{ }234x\text{ }-\text{ }119\] done
clear
D)
\[{{x}^{3}}-\text{ }18{{x}^{2}}+\text{ }108x\text{ }+114\] done
clear
E)
None of these done
clear
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question_answer 22)
What should be added to \[\frac{\mathbf{1}}{{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-12x+32}}\] to get \[\frac{\mathbf{1}}{{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-11x+30}}\]
A)
\[\frac{2{{x}^{{{2}^{{}}}}}-25x+96}{(x-6)(x-5)(x-4)(x-8)}\] done
clear
B)
\[\frac{2{{x}^{{{2}^{{}}}}}-25x-66}{(x-6)(x-5)(x-4)(x-8)}\] done
clear
C)
\[\frac{2{{x}^{{{2}^{{}}}}}-25x+66}{(x-6)(x-5)(x-4)(x-8)}\] done
clear
D)
\[\frac{2}{(x-6)(x-5)(x-4)(x-8)}\] done
clear
E)
None of these done
clear
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question_answer 23)
If \[p(x)={{x}^{2}}+x+1\] and \[q(x)={{x}^{3}}-x+1,\] then the HCF of p(a) - p(b) and q(a)-q(b) is ___________
A)
\[a+b+1\] done
clear
B)
\[ab+1\] done
clear
C)
\[a-b\] done
clear
D)
\[a+b\] done
clear
E)
None of these done
clear
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question_answer 24)
If \[({{x}^{2}}+x-1)\] is a factor of \[{{x}^{4}}+9{{x}^{3}}+q{{x}^{2}}-8x+5\] then find the values of p and q.
A)
\[p=-\,3,\text{ }q=4\] done
clear
B)
\[p=4,\text{ }q=-\,3\] done
clear
C)
\[p=2,\text{ }q=-\,4\] done
clear
D)
\[p=-\,4,\text{ }q=2\] done
clear
E)
None of these done
clear
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question_answer 25)
If the zeroes of the algebraic expression\[3a{{x}^{2}}+x(3b+5a)+5b\]are\[\frac{-3}{7}\]and\[\frac{-\,5}{3}\], then find the value of\[\frac{\mathbf{a}}{\mathbf{b}}\].
A)
\[\frac{1}{3}\] done
clear
B)
\[\frac{4}{5}\] done
clear
C)
\[\frac{7}{3}\] done
clear
D)
3 done
clear
E)
None of these done
clear
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question_answer 26)
If degree of both p(x) and [p(x) + q(x)] is 15 then degree of q(x) can be
A)
12 done
clear
B)
10 done
clear
C)
15 done
clear
D)
any one of the above done
clear
E)
None of these done
clear
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question_answer 27)
If the LCM of p(x) and q(x) is \[{{\mathbf{a}}^{\mathbf{9}}}\text{ }-\text{ }{{\mathbf{b}}^{\mathbf{9}}}\]then their HCF can be
A)
(a - b) done
clear
B)
\[\left( {{a}^{2}}+{{b}^{2}}+ab \right)\] done
clear
C)
\[{{a}^{6}}+\text{ }{{b}^{6}}+\text{ }{{a}^{3}}{{b}^{3}}\] done
clear
D)
All the above done
clear
E)
None of these done
clear
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question_answer 28)
If \[m=\frac{a+1}{a-1}\] and \[n=\frac{a-1}{a+1},\] then \[{{m}^{2}}+{{n}^{2}}-3mn\] is equal to
A)
\[\frac{-{{a}^{4}}+18{{a}^{2}}-1}{{{a}^{4}}-2{{a}^{2}}+1}\] done
clear
B)
\[\frac{{{a}^{4}}-9{{a}^{2}}+3}{{{a}^{4}}+2{{a}^{2}}+1}\] done
clear
C)
\[\frac{{{a}^{4}}+9{{a}^{2}}-3}{{{a}^{4}}-2{{a}^{2}}+1}\] done
clear
D)
\[\frac{-{{a}^{4}}+16{{a}^{2}}+1}{{{a}^{4}}-2{{a}^{2}}+1}\] done
clear
E)
None of these done
clear
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question_answer 29)
Solve \[\frac{{{\mathbf{p}}^{\mathbf{2}}}{{\mathbf{(q-r)}}^{\mathbf{2}}}}{{{\mathbf{(p+r)}}^{\mathbf{2}}}\mathbf{-}{{\mathbf{q}}^{\mathbf{2}}}}\mathbf{+}\frac{{{\mathbf{q}}^{\mathbf{2}}}\mathbf{-(p-r}{{\mathbf{)}}^{\mathbf{2}}}}{{{\mathbf{(p}+\mathbf{q)}}^{\mathbf{2}}}\mathbf{-}{{\mathbf{r}}^{\mathbf{2}}}}\mathbf{+}\frac{{{\mathbf{r}}^{\mathbf{2}}}\mathbf{-(p-q}{{\mathbf{)}}^{\mathbf{2}}}}{{{\mathbf{(q+r)}}^{\mathbf{2}}}\mathbf{-}{{\mathbf{p}}^{\mathbf{2}}}}\]
A)
\[\frac{1}{p+q+r}\] done
clear
B)
p + q + r done
clear
C)
0 done
clear
D)
1 done
clear
E)
None of these done
clear
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question_answer 30)
Find the value of a - b so that \[8{{x}^{4}}+14{{x}^{3}}-a{{x}^{2}}+bx+2\] is exactly divisible by \[4{{x}^{2}}+3x-2\].
A)
4 done
clear
B)
6 done
clear
C)
9 done
clear
D)
\[-\]3 done
clear
E)
None of these done
clear
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question_answer 31)
If two zeroes of the polynomial \[f(x)={{x}^{4}}-2{{x}^{3}}-18{{x}^{2}}-6x+45\] are \[-\,\sqrt{3}\] and\[\,\sqrt{3}\] , then find the sum of other two zeroes.
A)
0 done
clear
B)
\[-\]1 done
clear
C)
\[-\]2 done
clear
D)
1 done
clear
E)
None of these done
clear
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question_answer 32)
If the zeroes of the polynomial \[{{x}^{3}}-15{{x}^{2}}+66x-80\] are \[\alpha ,\] \[\beta \] & \[\gamma \] and it is also given that \[2\beta =\alpha +\gamma \] then
A)
\[\alpha =4\] done
clear
B)
\[\gamma =3\] done
clear
C)
\[\gamma =7\] done
clear
D)
\[\alpha =2\] done
clear
E)
None of these done
clear
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question_answer 33)
If \[\alpha \] & \[\beta \] are the zeroes of the polynomial \[{{x}^{2}}+6x-k\] such that \[2\beta +\alpha =11\] then k is equal to
A)
18 done
clear
B)
\[-\]23 done
clear
C)
391 done
clear
D)
\[-\]391 done
clear
E)
None of these done
clear
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question_answer 34)
If p and q are the zeroes of the quadratic polynomial \[f(x)=c{{x}^{2}}+ax+b\] then the value of \[{{\mathbf{p}}^{\mathbf{4}}}+\text{ }{{\mathbf{q}}^{\mathbf{4}}}\]is ______
A)
\[\frac{{{({{a}^{2}}-2bc)}^{2}}-{{b}^{2}}{{c}^{2}}}{{{c}^{4}}}\] done
clear
B)
\[\frac{{{({{a}^{2}}-2bc)}^{2}}-2{{b}^{2}}{{c}^{2}}}{{{c}^{4}}}\] done
clear
C)
\[\frac{{{({{b}^{2}}-2ac)}^{2}}-{{a}^{2}}{{c}^{2}}}{{{c}^{4}}}\] done
clear
D)
\[\frac{{{({{b}^{2}}-2ac)}^{2}}-2{{a}^{2}}{{c}^{2}}}{{{c}^{4}}}\] done
clear
E)
None of these done
clear
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question_answer 35)
If on dividing the polynomial \[\mathbf{f(x)=}{{\mathbf{x}}^{\mathbf{3}}}\mathbf{-4}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{+7x-9}\] by a polynomial g(x), the quotient q(x) and the remainder r(x) are \[(x-3)\] and \[(2x-3)\] respectively, the polynomial g(x) is ____
A)
\[{{x}^{2}}+x+1\] done
clear
B)
\[{{x}^{2}}-x+2\] done
clear
C)
\[2{{x}^{2}}+x+1\] done
clear
D)
\[2{{x}^{2}}-x+2\] done
clear
E)
None of these done
clear
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question_answer 36)
If the zeroes of the polynomial \[f(x)=a{{x}^{3}}+3b{{x}^{2}}+3cx+d\] are in A.P. then \[2{{b}^{3}}+{{a}^{2}}d\] is equal to _______
A)
\[{{a}^{2}}bc\] done
clear
B)
\[3abc\] done
clear
C)
\[2{{b}^{2}}ac\] done
clear
D)
\[abc\] done
clear
E)
None of these done
clear
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question_answer 37)
If f(x) = 3x4 + 6x3 - 2x2 - l0x - 5 and two of its zeroes are - 1, - 1, then the other two zeroes are _______
A)
\[\sqrt{\frac{3}{5},}-\sqrt{\frac{3}{5}}\] done
clear
B)
\[\sqrt{\frac{2}{5},}-\sqrt{\frac{2}{5}}\] done
clear
C)
\[\sqrt{\frac{5}{3},}-\sqrt{\frac{5}{3}}\] done
clear
D)
\[\sqrt{\frac{5}{4},}-\sqrt{\frac{5}{4}}\] done
clear
E)
None of these done
clear
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question_answer 38)
If \[\alpha ,\,\,\beta ,\,\,\gamma \] are the zeroes of the polynomial \[p(x)={{x}^{3}}-a{{x}^{2}}+bx-c,\] then\[\frac{1}{\alpha \beta }+\frac{1}{\beta \gamma }+\frac{1}{\alpha \gamma }=\]__________
A)
\[\frac{a}{b}\] done
clear
B)
\[\frac{b}{c}\] done
clear
C)
\[\frac{a}{c}\] done
clear
D)
\[\frac{c}{d}\] done
clear
E)
None of these done
clear
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question_answer 39)
The graph of a polynomial f(x) is shown below: The number of real zeroes of the polynomial f(x) is _________
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
E)
None of these done
clear
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question_answer 40)
The graph of a polynomial \[p(x)=a{{x}^{2}}+bx+c\] is shown below: Based on the above graph which one is correct?
A)
a > 0, b > 0, c > 0 done
clear
B)
a < 0, b < 0, c > 0 done
clear
C)
a < 0, b < 0, c < 0 done
clear
D)
a > 0, b < 0, c > 0 done
clear
E)
None of these done
clear
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