10th Class Mathematics Polynomials Question Bank

done Polynomials Total Questions - 55

• question_answer1)
  Which of the following is a cubic polynomial whose zeros are (-1), (-2) and (-3)?
  A)
   \[{{p}^{3}}-6\] done clear
  B)
   \[{{p}^{3}}-6{{p}^{2}}+6\] done clear
  C)
   \[{{p}^{3}}+6{{p}^{2}}+11p+6\] done clear
  D)
   \[{{p}^{3}}-6{{p}^{3}}-11p-6\] done clear
  View Solution play_arrow

• question_answer2)
  2 and (-2) are two zeros of the polynomial\[\text{34}\,{{\text{m}}^{\text{4}}}-\text{4m}+\text{12}0\]. What are the other two zeros of the polynomial?
  A)
   5,-6                       done clear
  B)
          -5, 6 done clear
  C)
   -5,-6                      done clear
  D)
          5, 6 done clear
  View Solution play_arrow

• question_answer3)
  Find the value of the polynomial \[p(x)={{x}^{2}}+3x-2\]when x = (-1).
  A)
   -4                                           done clear
  B)
   3 done clear
  C)
   4                             done clear
  D)
          6 done clear
  View Solution play_arrow

• question_answer4)
  For what value of 'm' is one zero of the polynomial\[({{m}^{2}}+9){{x}^{2}}+13x+6m\], the reciprocal of the other?
  A)
   9                             done clear
  B)
          -3 done clear
  C)
   6                                             done clear
  D)
   3 done clear
  View Solution play_arrow

• question_answer5)
  Identify the polynomial whose sum of zeros is (-5) and their product is 6.
  A)
   \[{{x}^{2}}-4x-12\] done clear
  B)
                          \[{{x}^{2}}+4x+12\] done clear
  C)
   \[{{p}^{2}}+6p-4\]     done clear
  D)
          \[{{x}^{2}}-5x+6\] done clear
  View Solution play_arrow

• question_answer6)
  \[\alpha \]and\[\beta \]are the zeros of a polynomial, such that\[\alpha +\beta =6\]and\[\alpha \beta =4\]. Identify the polynomial.
  A)
   \[{{x}^{2}}-6x+4\]           done clear
  B)
          \[{{a}^{2}}+6a+4\] done clear
  C)
   \[{{p}^{2}}+6p-4\]          done clear
  D)
          \[{{m}^{2}}-6m-4\] done clear
  View Solution play_arrow

• question_answer7)
  Identify the zeros of the polynomial\[p(t)={{t}^{3}}-3{{t}^{2}}-10t+24\]
  A)
   -2,-3,-4                done clear
  B)
          -2, -3, 4 done clear
  C)
   2,-3, 4                   done clear
  D)
          2, -3, -4 done clear
  View Solution play_arrow

• question_answer8)
  What is the quotient when\[\text{2}{{\text{m}}^{\text{2}}}-\text{m}+\text{3}\]is divided by (2 - m) leaving a remainder 9?
  A)
   -2m + 3                done clear
  B)
          -(2m - 3) done clear
  C)
   2m + 3                  done clear
  D)
          -(2m + 3) done clear
  View Solution play_arrow

• question_answer9)
  Choose the cubic polynomial whose zeros are-2,3 and 5.
  A)
   \[{{\text{p}}^{\text{3}}}-\text{6}{{\text{p}}^{\text{2}}}-\text{p}+\text{3}0\] done clear
  B)
   \[{{\text{x}}^{\text{3}}}\text{+6}{{\text{x}}^{\text{2}}}-\text{x-3}0\] done clear
  C)
   \[{{\text{x}}^{\text{3}}}-\text{6}{{\text{x}}^{\text{2}}}+\text{x}-\text{3}0\] done clear
  D)
   \[{{\text{p}}^{\text{3}}}+\text{6}{{\text{p}}^{\text{2}}}+\text{p}-\text{3}0\] done clear
  View Solution play_arrow

• question_answer10)
  Choose the zeros of the polynomial\[6{{x}^{2}}-7x-3\]
  A)
   \[\frac{1}{3},\frac{-1}{2}\]           done clear
  B)
          \[\frac{-1}{3},\frac{3}{2}\] done clear
  C)
   \[\frac{-1}{3},\frac{-1}{2}\]         done clear
  D)
          \[\frac{1}{3},\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer11)
  Which of the following is the division algorithm of polynomials if dividend = f(x), divisor = p(x), quotient = q(x) and remainder = r(x)?
  A)
   f(x) = r(x) p(x) + q(x) done clear
  B)
   f(x) = p(x) q(x) + r(x) done clear
  C)
   f(x) = p(x) q(x) - r(x) done clear
  D)
   f(x) = p(x) r(x) - q(x) done clear
  View Solution play_arrow

• question_answer12)
  a, p and y are the zeros of a cubic polynomial. If \[\alpha +\beta +\gamma =2\],\[\alpha \beta +\beta \gamma +\gamma \alpha =(-7)\]and\[\alpha \beta \gamma =(-14)\] find the polynomial.
  A)
   \[{{x}^{3}}-2{{x}^{2}}-7x+14\] done clear
  B)
   \[{{m}^{3}}+2{{m}^{2}}-7m-14\] done clear
  C)
   \[{{n}^{3}}-2{{n}^{2}}+7n-14\] done clear
  D)
   \[{{y}^{3}}+2{{y}^{2}}-7y-14\] done clear
  View Solution play_arrow

• question_answer13)
  Find the remainder when\[\text{5}{{\text{p}}^{\text{3}}}-\text{13}{{\text{p}}^{\text{2}}}+\text{21p}-14\]is divided by\[(\text{3}-\text{2p}+{{\text{p}}^{\text{2}}})\].
  A)
   -5           done clear
  B)
          -15 done clear
  C)
   -10                         done clear
  D)
          5 done clear
  View Solution play_arrow

• question_answer14)
  The polynomial \[{{\text{a}}^{\text{3}}}-\text{3}{{\text{a}}^{\text{2}}}+\text{a}+\text{2}\]is divided by a polynomial g[a].The quotient and remainder obtained are (a - 2) and (-2a + 4) respectively. Find g[a].
  A)
   \[{{\text{a}}^{\text{2}}}+\text{a}+\text{1}\]       done clear
  B)
          \[{{\text{a}}^{\text{2}}}-\text{a}+\text{1}\] done clear
  C)
   \[{{\text{a}}^{\text{2}}}-\text{a}-\text{1}\]        done clear
  D)
          \[{{\text{a}}^{\text{2}}}+\text{a}-\text{1}\] done clear
  View Solution play_arrow

• question_answer15)
  Choose the zeros of the polynomial whose graph is given.
  A)
   1.-1.2                    done clear
  B)
          -2, 1, 3 done clear
  C)
   -2, 0, 3                  done clear
  D)
          -2, 2, 3 done clear
  View Solution play_arrow

• question_answer16)
  What is the nature of the zeros of the quadratic polynomial\[{{x}^{2}}+\text{88}x+\text{125}\]?
  A)
   Both positive done clear
  B)
   Both negative done clear
  C)
   One positive, one negative done clear
  D)
   Cannot be said done clear
  View Solution play_arrow

• question_answer17)
  If\[\alpha \]and\[\beta \]are the zeros of\[p(x)=2{{x}^{2}}-6+6x\], which of the following is correct?
  A)
   \[\alpha +\beta <\alpha \beta \]              done clear
  B)
          \[\alpha +\beta >\alpha \beta \] done clear
  C)
   \[\alpha +\beta >\alpha \beta \]              done clear
  D)
          \[\alpha +\beta =\alpha \beta \] done clear
  View Solution play_arrow

• question_answer18)
  If a polynomial p(x) is divided by another polynomial g(x),with a quotient q(x) and remainder r(x),then p(x) = q(x) g(x)+ r(x). What is the condition that r(x) must satisfy?
  A)
   r(x) = 0 done clear
  B)
   r(x) = 0 or deg of r(x) > deg g(x) always. done clear
  C)
   Either r(x) = 0 or deg (g(x)) > deg r(x) done clear
  D)
   r(x) = g(x) done clear
  View Solution play_arrow

• question_answer19)
  If P and Q are the zeros of the polynomial \[a{{x}^{2}}+bx+c\], what is the value of \[{{\text{P}}^{\text{2}}}+{{\text{Q}}^{\text{2}}}\]?
  A)
   \[\frac{{{b}^{2}}+2ac}{{{a}^{2}}}\]                           done clear
  B)
   \[\frac{{{a}^{2}}+2bc}{{{b}^{2}}}\] done clear
  C)
   \[\frac{{{a}^{2}}-2bc}{{{b}^{2}}}\]            done clear
  D)
          \[\frac{{{b}^{2}}-2ac}{{{a}^{2}}}\] done clear
  View Solution play_arrow

• question_answer20)
  The zeros of the polynomial \[{{\text{n}}^{\text{3}}}+\text{9}\,{{\text{n}}^{\text{2}}}+23\,n\]\[+15\]are a - d, a and a + d. What is the value of 'a'?
  A)
   4                                             done clear
  B)
   -3 done clear
  C)
   6                             done clear
  D)
          3 done clear
  View Solution play_arrow

• question_answer21)
  Find the zeros of the polynomial\[4{{n}^{2}}+5\sqrt{2}n-3\]
  A)
   \[\frac{-3\sqrt{2}}{2},\frac{\sqrt{2}}{4}\]                              done clear
  B)
   \[3\sqrt{2},\sqrt{2}\] done clear
  C)
   \[\frac{3\sqrt{2}}{4},\frac{\sqrt{2}}{4}\]               done clear
  D)
          \[-3\sqrt{2},\sqrt{2}\] done clear
  View Solution play_arrow

• question_answer22)
  Which of the following is the graph of a linear polynomial?
  A)
    done clear
  B)
           done clear
  C)
         done clear
  D)
           done clear
  View Solution play_arrow

• question_answer23)
  Choose the graph of a quadratic polynomial.
  A)
    done clear
  B)
           done clear
  C)
    done clear
  D)
           done clear
  View Solution play_arrow

• question_answer24)
  If one zero of the quadratic polynomial \[2{{x}^{2}}-(3k+1)x-9\]is negative of the other, find the value of 'k'.
  A)
   \[-\frac{1}{6}\]                 done clear
  B)
          3 done clear
  C)
   \[\frac{1}{4}\]                   done clear
  D)
          \[-\frac{1}{3}\] done clear
  View Solution play_arrow

• question_answer25)
  Identify the quadratic polynomial with no zeros.
  A)
     done clear
  B)
    done clear
  C)
    done clear
  D)
           done clear
  View Solution play_arrow

• question_answer26)
  The graphs of y= f(x) are given in figures. For which of these is f(x) neither linear nor quadratic?
  A)
    done clear
  B)
           done clear
  C)
    done clear
  D)
           done clear
  View Solution play_arrow

• question_answer27)
  A cubic polynomial \[a{{x}^{3}}+b{{x}^{2}}+cx+d\] with real coefficients has at the most 'n' real zeros. Find the value of 'n'.
  A)
   2                             done clear
  B)
          1     done clear
  C)
   3                             done clear
  D)
          4 done clear
  View Solution play_arrow

• question_answer28)
  Find the sum of zeros of the polynomial \[2{{x}^{2}}-9\].
  A)
   0             done clear
  B)
          1    done clear
  C)
  -1                            done clear
  D)
          2 done clear
  View Solution play_arrow

• question_answer29)
  If a and p are two zeros of the quadratic polynomial \[p(x)=2{{x}^{2}}-3x+7\], find the value of \[{{\text{a}}^{\text{3}}}+{{\text{p}}^{\text{3}}}\].
  A)
   \[\frac{37}{2}\]                done clear
  B)
          \[\frac{-37}{2}\] done clear
  C)
   \[\frac{-99}{8}\]                      done clear
  D)
          \[\frac{27}{2}\] done clear
  View Solution play_arrow

• question_answer30)
  What is the relation between the zeros and the coefficients of the polynomial \[4\sqrt{3}{{x}^{2}}+5x-2\sqrt{3}\]?
  A)
  \[\text{Sum of zeros }=\frac{-(\text{coefficient of x})}{(\text{coefficient of }{{\text{x}}^{\text{2}}})}\] done clear
  B)
   \[\text{Sum of zeros }=\frac{(\text{coefficient of x})}{(\text{coefficient of }{{\text{x}}^{\text{2}}})}\] done clear
  C)
   \[\text{Sum of zeros }=\frac{(\text{coefficient of }{{\text{x}}^{2}})}{(\text{coefficient of x})}\] done clear
  D)
   \[\text{Sum of zeros }=\frac{(\text{coefficient of }{{\text{x}}^{2}})}{cons\tan t}\] done clear
  View Solution play_arrow

• question_answer31)
  If the sum of the squares of zeros of the polynomial \[6{{x}^{2}}+x+k\]is \[\frac{25}{36}\], find the value of 'k'.
  A)
   2                                             done clear
  B)
   -2 done clear
  C)
   24                          done clear
  D)
          ? 24 done clear
  View Solution play_arrow

• question_answer32)
  Choose the graph of a cubic polynomial.
  A)
                 done clear
  B)
    done clear
  C)
    done clear
  D)
           done clear
  View Solution play_arrow

• question_answer33)
  Find a quadratic polynomial, whose sum and product of zeros are\[\frac{-10}{\sqrt{3}}\]and 7 respectively.
  A)
   \[{{x}^{2}}+\frac{10}{\sqrt{3}}x+\frac{7}{\sqrt{3}}\] done clear
  B)
   \[\sqrt{3}{{x}^{2}}-10x+7\sqrt{3}\] done clear
  C)
   \[\sqrt{3}{{x}^{2}}+10x+7\sqrt{3}\] done clear
  D)
   \[{{x}^{2}}+10x+7\sqrt{3}\] done clear
  View Solution play_arrow

• question_answer34)
  Find the quadratic polynomial one of whose zeros is\[\frac{\sqrt{3}}{4}\]and the product of zeros is\[\frac{1}{2}\].
  A)
   \[4\sqrt{3}{{x}^{2}}+5x+2\sqrt{3}\] done clear
  B)
   \[{{x}^{2}}+\frac{5}{4\sqrt{3}}x-\frac{1}{2}\] done clear
  C)
   \[4\sqrt{3}-5x+2\sqrt{3}\] done clear
  D)
   \[2{{x}^{2}}+\frac{5}{4\sqrt{3}}x-\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer35)
  A quadratic polynomial\[\text{f(x)}=\text{2}\times \text{2}-\text{mx}+n\]has \[\alpha \] and \[\beta \] as its two zeros. Find the value of\[~{{\alpha }^{\text{2}}}+{{\beta }^{\text{2}}}\].
  A)
   \[\frac{1}{8}({{m}^{2}}-4n)\]      done clear
  B)
          \[\frac{1}{4}({{m}^{2}}+4n)\] done clear
  C)
   \[\frac{1}{4}({{m}^{2}}-4n)\] done clear
  D)
          \[\frac{1}{3}({{m}^{2}}+4n)\] done clear
  View Solution play_arrow

• question_answer36)
  The zeros of a quadratic polynomial\[f(x)=2{{x}^{2}}-mx+n\]are\[\alpha \]and\[\beta \]such that\[\alpha -\beta =3\]. Find the value of 'k'.
  A)
   10                          done clear
  B)
          2 done clear
  C)
   5                             done clear
  D)
          15 done clear
  View Solution play_arrow

• question_answer37)
  The zeros of the quadratic polynomial \[\text{p(x)}=\text{6}{{\text{x}}^{\text{2}}}+\text{mx}+\text{2n}\]are\[-\frac{3}{2}\]and\[\frac{4}{3}\].Find the respective values of 'm' and 'n'.
  A)
   2 and 3                 done clear
  B)
          6 and 4 done clear
  C)
   3 and 5                 done clear
  D)
          1 and 6 done clear
  View Solution play_arrow

• question_answer38)
  If one of the zeros of the quadratic polynomial \[\text{f(x)}=\text{3}{{\text{x}}^{\text{2}}}-\text{2}0\text{x}+\text{3p}+\text{4}\]is four times the other, find the value of 'p'.
  A)
   \[\frac{76}{6}\]                                done clear
  B)
   \[\frac{52}{9}\] done clear
  C)
   \[\frac{25}{4}\]                done clear
  D)
          \[\frac{36}{5}\] done clear
  View Solution play_arrow

• question_answer39)
  The zeros of the quadratic polynomial\[{{x}^{2}}+4x+k\]are\[\alpha \]and\[\beta \]. Find the value of 'k' if\[\text{5}\alpha +\text{2}\beta =\text{1}\].
  A)
   20                          done clear
  B)
          ? 11 done clear
  C)
   -21                         done clear
  D)
          35 done clear
  View Solution play_arrow

• question_answer40)
  Find\[{{\alpha }^{-1}}+{{\beta }^{-1}}\]if\[\alpha \]and\[\beta \]are the zeros of the polynomial\[\text{f(x)}=\text{9}{{\text{x}}^{\text{2}}}-\text{3x}-\text{2}\].
  A)
   \[\frac{-3}{2}\]                 done clear
  B)
          \[\frac{5}{3}\] done clear
  C)
   \[\frac{-2}{7}\]                 done clear
  D)
          \[\frac{2}{7}\] done clear
  View Solution play_arrow

• question_answer41)
  Find the cubic polynomial with the sum of its zeros, sum of the products of its zeros taken two at a time and the product  of its zeros as \[\frac{1}{4},-\frac{3}{2}\] and \[\frac{9}{16}\]respectively.
  A)
   \[{{x}^{2}}-\frac{1}{2}{{x}^{2}}-3x+\frac{9}{16}\] done clear
  B)
   \[16{{x}^{3}}-4{{x}^{2}}-24x-9\] done clear
  C)
   \[{{x}^{3}}+\frac{1}{4}{{x}^{2}}-4x+16\] done clear
  D)
   \[16{{x}^{3}}-5{{x}^{2}}+21x-7\] done clear
  View Solution play_arrow

• question_answer42)
  When is a real number 'a' called the zero of the polynomial f(x) ?
  A)
   f(0)=a                   done clear
  B)
          f=a done clear
  C)
   f=0        done clear
  D)
          f=f(0) done clear
  View Solution play_arrow

• question_answer43)
  Which of the following is the quadratic polynomial whose zeros are\[\frac{1}{3}\]and\[\frac{-2}{5}\]?
  A)
   \[15{{x}^{2}}+x-2\]    done clear
  B)
          \[15{{x}^{2}}+5x-6\] done clear
  C)
   \[15{{x}^{2}}-5x+6\]   done clear
  D)
          \[15{{x}^{2}}-x+2\] done clear
  View Solution play_arrow

• question_answer44)
  If the sum of the zeros of the polynomial \[\text{f(x)}=({{\text{k}}^{\text{2}}}-\text{14}){{\text{x}}^{\text{2}}}-\text{2x}-\text{12}\]is 1, which is one of the possible values of 'k' ?
  A)
   \[\sqrt{14}\]                      done clear
  B)
          -14 done clear
  C)
   2            done clear
  D)
          -4 done clear
  View Solution play_arrow

• question_answer45)
  If \[\alpha \]and \[\beta \]are the zeros of the polynomial, \[f(x)={{x}^{2}}+ax-b\] find the polynomial having zeros \[\frac{1}{\alpha }\]and\[\frac{1}{\beta }\].
  A)
   \[ab{{x}^{2}}+bx-a\] done clear
  B)
          \[{{x}^{2}}-\frac{a}{b}x-\frac{1}{b}\] done clear
  C)
   \[ab{{x}^{2}}-bx+a\] done clear
  D)
          \[{{x}^{2}}-\frac{b}{a}x+\frac{1}{a}\] done clear
  View Solution play_arrow

• question_answer46)
  If the product of two of the zeros of the polynomial \[\text{p(x)}={{\text{x}}^{\text{3}}}+\text{6}{{\text{x}}^{\text{2}}}-\text{x}-\text{3}0\]i\[-\,\text{6}\], what is the third zero of p(x)?
  A)
   6                             done clear
  B)
          5 done clear
  C)
   - 1                          done clear
  D)
          ? 5 done clear
  View Solution play_arrow

• question_answer47)
  If \[\alpha ,\beta \] and y are the zeros of the polynomial\[\text{6}{{\text{x}}^{\text{3}}}+\text{31}{{\text{x}}^{\text{2}}}-\text{29x}+\text{6}\], what is the value of\[(\alpha \beta +\beta \gamma +\gamma \alpha )\]?
  A)
  - 29                        done clear
  B)
  \[\frac{31}{6}\] done clear
  C)
  \[\frac{-29}{6}\]               done clear
  D)
  - 1 done clear
  View Solution play_arrow

• question_answer48)
  Which of the following is a zero of the cubic polynomial\[\text{f(x)}={{\text{x}}^{\text{3}}}-\text{3x}+\text{2}\]?
  A)
  - 2                          done clear
  B)
  - 1 done clear
  C)
   0                             done clear
  D)
  2 done clear
  View Solution play_arrow

• question_answer49)
  Identify polynomials from the following.

  (i) \[\frac{2}{{{x}^{2}}}-3x+2\]

  (ii) \[2{{x}^{1}}+3-4x\]

  (iii) \[\frac{1}{3}{{x}^{2}}-3\]

  (iv) \[\sqrt{x}-6\]

  A)
   (i) and (ii) only done clear
  B)
          (ii) and (iii) only done clear
  C)
   (i) and (iii) only done clear
  D)
          (ii) and (iv) only done clear
  View Solution play_arrow

• question_answer50)
  The general quadratic polynomial is\[p(x)=\]\[a{{x}^{2}}+bx+c,a\ne 0\]. If\[\alpha \]and\[\beta \]are its zeros, which of the following is true?
  A)
   \[\alpha +\beta =\frac{-b}{a}\] done clear
  B)
          \[\alpha -\beta =\frac{b}{a}\] done clear
  C)
   \[\alpha \beta =\frac{a}{c}\]      done clear
  D)
          \[\frac{\alpha }{\beta }=\frac{c}{a}\] done clear
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• question_answer51)
  \[\alpha \],\[\beta \]and y are the zeros of the polynomial\[a{{x}^{3}}+b{{x}^{2}}+cx+d,a\ne 0\]. What is\[\alpha +\beta +\gamma \]?
  A)
   \[\frac{-d}{a}\]                 done clear
  B)
          \[\frac{c}{a}\] done clear
  C)
   \[\frac{-b}{a}\]                 done clear
  D)
          \[\frac{c}{d}\] done clear
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• question_answer52)
  If a, p and y are the zeros of p(x), which of the following is true?
  A)
   \[p(x)=(x-\alpha )(x-\beta )(x-\gamma )\] done clear
  B)
   \[p(x)=(x+\alpha )(x-\beta )(x-\gamma )\] done clear
  C)
   \[p(x)=(x+\alpha )(x+\beta )(x-\gamma )\] done clear
  D)
   \[p(x)=(x+\alpha )(x+\beta )(x+\gamma )\] done clear
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• question_answer53)
  Find a quadratic polynomial whose sum and product of zeros are both 1.
  A)
   \[{{x}^{2}}-x+1\]                             done clear
  B)
   \[{{x}^{2}}-x-1\] done clear
  C)
   \[{{x}^{2}}+x-1\]             done clear
  D)
          \[{{x}^{2}}+x+1\] done clear
  View Solution play_arrow

• question_answer54)
  The remainder when\[{{x}^{4}}-5x+6\]is divided by\[2-{{x}^{2}}\]is of the form\[px+q\]. What are the respective values of 'p' and 'q'?
  A)
   10, 5                      done clear
  B)
          -5, 10 done clear
  C)
   -10, 5                    done clear
  D)
          -10, -5 done clear
  View Solution play_arrow

• question_answer55)
  Which of the following is not correct?
  A)
   The degree of a zero polynomial is zero. done clear
  B)
   The polynomial\[{{x}^{4}}+1\]has 4 zeros. done clear
  C)
   The degree of a cubic polynomial is 3. done clear
  D)
   A quadratic polynomial has two zeros. done clear
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