10th Class Mathematics Quadratic Equations Question Bank

done Quadratic Equations Total Questions - 50

• question_answer1)
  Identify the quadratic equation from the following.
  A)
   \[p+\frac{1}{p}=1,p\ne 0\]         done clear
  B)
   \[{{p}^{2}}+\frac{1}{p}=1,p\ne 0\] done clear
  C)
   \[{{x}^{2}}-\frac{1}{x}=1,x\ne 0\] done clear
  D)
          \[{{x}^{2}}+2\sqrt{x}-1=0\] done clear
  View Solution play_arrow

• question_answer2)
  Find the roots of the quadratic equation
  A)
   \[\frac{-1}{2},1\]             done clear
  B)
          \[-1,\frac{1}{2}\]             done clear
  C)
   \[\frac{1}{2},1\]                               done clear
  D)
          \[-1,\frac{-1}{2}\] done clear
  View Solution play_arrow

• question_answer3)
  Which of the following statements is correct?
  A)
   \[x=1\]is a root of \[2{{x}^{2}}+3x+1=0\]. done clear
  B)
   \[x=2\]is not a root of\[6{{x}^{2}}+7x-5=0\]. done clear
  C)
   \[x=-1\]is a root of \[3{{x}^{2}}-x-1=0\]. done clear
  D)
   \[x=-\frac{2}{5}\]is not a root of \[5{{x}^{2}}-8x-4=0\]. done clear
  View Solution play_arrow

• question_answer4)
  Find the value of 'p' for which \[m=\frac{1}{\sqrt{3}}\]is a root of the equation \[p{{m}^{2}}+(\sqrt{3}-\sqrt{2})m-1=0\]
  A)
   \[\sqrt{3}\]                                        done clear
  B)
   \[\sqrt{2}\] done clear
  C)
   \[\sqrt{6}\]                        done clear
  D)
          \[\sqrt{7}\] done clear
  View Solution play_arrow

• question_answer5)
  For what respective values of 'm' and 'n' are \[x=\frac{-2}{5}\] and \[x=\frac{5}{3}\] the roots of\[m{{x}^{2}}+nx-10=0\]?
  A)
   15,-19                   done clear
  B)
          -19, 15 done clear
  C)
   19,-15                   done clear
  D)
          -15, 19 done clear
  View Solution play_arrow

• question_answer6)
  The sides of two square plots are \[(2x-1)m\]and\[(5x+4)m\]. The area of the second square plot is 9 times the area of the first square plot. Find the side of the larger plot.
  A)
   15m                      done clear
  B)
   13m done clear
  C)
   31 m     done clear
  D)
          39m done clear
  View Solution play_arrow

• question_answer7)
  What are the roots of \[\text{17}{{\text{a}}^{\text{2}}}-\text{2}0\text{a}+\text{1}0=\text{1}0{{\text{a}}^{\text{2}}}+\text{2a}+\text{7}\]?
  A)
   \[\frac{1}{7},3\]                               done clear
  B)
          \[3,\frac{-1}{7}\] done clear
  C)
   \[\frac{-1}{7},-3\]            done clear
  D)
          \[-3,-\frac{1}{7}\] done clear
  View Solution play_arrow

• question_answer8)
  Identify the factors of\[\frac{4{{x}^{2}}}{5}=4x-5\].
  A)
   \[\frac{2}{5},\frac{2}{5}\]            done clear
  B)
          \[\frac{-5}{2},\frac{5}{2}\] done clear
  C)
   \[\frac{5}{2},\frac{5}{2}\]            done clear
  D)
          \[\frac{-2}{5},\frac{2}{5}\] done clear
  View Solution play_arrow

• question_answer9)
  The age of a man is the square of his son's age. A year ago, the man's age was eight times the age of his son. What is the present age of the man?
  A)
   47 years              done clear
  B)
          49 years done clear
  C)
   36 years              done clear
  D)
          48 years done clear
  View Solution play_arrow

• question_answer10)
  Find two consecutive even numbers whose product is double that of the greater number.
  A)
   1, 3                                        done clear
  B)
   4, 6  done clear
  C)
   2, 4                        done clear
  D)
          6, 8 done clear
  View Solution play_arrow

• question_answer11)
  The length and breadth of a rectangle are (3k + 1) cm and (2k - 1) cm respectively. Find the perimeter of the rectangle if its area is\[\text{144}\,\text{c}{{\text{m}}^{\text{2}}}\].
  A)
   50 cm                   done clear
  B)
   10 cm done clear
  C)
   32 cm   done clear
  D)
          25 cm done clear
  View Solution play_arrow

• question_answer12)
  The sum of squares of two consecutive positive even numbers is 340. Find them.
  A)
   12, 14                   done clear
  B)
   12, 10 done clear
  C)
   10, 8      done clear
  D)
          14, 16 done clear
  View Solution play_arrow

• question_answer13)
  Find two consecutive positive odd numbers, the sum of whose squares is 514.
  A)
   11, 13   done clear
  B)
          15, 17 done clear
  C)
   11, 9      done clear
  D)
                          13, 15 done clear
  View Solution play_arrow

• question_answer14)
  The area of a rectangular cardboard is \[\text{8}0\text{ c}{{\text{m}}^{\text{2}}}\]. If its perimeter is 36 cm, find its length.
  A)
   40 cm   done clear
  B)
          10 cm done clear
  C)
   20 cm                   done clear
  D)
   8 cm done clear
  View Solution play_arrow

• question_answer15)
  Find two consecutive integers whose product is 600.
  A)
   30, 20   done clear
  B)
          50, 12 done clear
  C)
   15, 40   done clear
  D)
          24, 25 done clear
  View Solution play_arrow

• question_answer16)
  Find the present age of a boy whose age 12 years from now will be the square of his present age.
  A)
   5 years                 done clear
  B)
          7 years done clear
  C)
   4 years                 done clear
  D)
          6 years done clear
  View Solution play_arrow

• question_answer17)
  Identify the correct statement.
  A)
   The roots of the quadratic equation\[2{{y}^{2}}+9y=0\]are 0 and\[\frac{-9}{2}\]. done clear
  B)
   The value of 'k' for which \[\text{4}{{\text{m}}^{\text{2}}}+\text{k}-\text{15}=0\] has a root m = 3 is 7. done clear
  C)
   The quadratic equation\[{{(4x-11)}^{2}}=0\]has two distinct roots. done clear
  D)
   \[7{{x}^{2}}-12x-18=0\]is not a quadratic equation. done clear
  View Solution play_arrow

• question_answer18)
  Find the roots of\[3{{x}^{2}}-2\sqrt{6x}+2=0\].
  A)
   \[\frac{2}{\sqrt{3}},\frac{2}{\sqrt{3}}\]                  done clear
  B)
   \[\frac{\sqrt{2}}{\sqrt{3}},\frac{\sqrt{2}}{\sqrt{3}}\] done clear
  C)
   \[\frac{\sqrt{2}}{3},\frac{\sqrt{3}}{2}\]  done clear
  D)
          \[\frac{\sqrt{2}}{3},\frac{\sqrt{3}}{3}\] done clear
  View Solution play_arrow

• question_answer19)
  Divide 63 into two parts such that their product is 962.
  A)
   24, 3C                                   done clear
  B)
   28, 35 done clear
  C)
   26, 37                   done clear
  D)
          27, 36 done clear
  View Solution play_arrow

• question_answer20)
  Which of the following is a quadratic equation?
  A)
   \[x-\frac{5}{x}={{x}^{2}}\]                           done clear
  B)
   \[{{x}^{2}}+\frac{2}{{{x}^{2}}}=1\] done clear
  C)
   \[2{{x}^{2}}+3\sqrt{x}+4=0\]     done clear
  D)
   \[{{x}^{2}}-1=2{{x}^{2}}+4\] done clear
  View Solution play_arrow

• question_answer21)
  The quadratic equation\[a{{x}^{2}}+bx+c=0\]has no real root. Which of the following is true?
  A)
   \[~{{\text{b}}^{\text{2}}}-\text{4ac}<0\]             done clear
  B)
   \[{{\text{b}}^{\text{2}}}-\text{4ac}=0\] done clear
  C)
   \[{{\text{b}}^{\text{2}}}-\text{4ac}>0\]    done clear
  D)
          \[{{\text{b}}^{\text{2}}}+\text{4ac}<0\] done clear
  View Solution play_arrow

• question_answer22)
  What is the nature of the roots of the quadratic equation\[25{{x}^{2}}-49=0\]?
  A)
   Real and distinct done clear
  B)
   Real and equal done clear
  C)
   Irrational done clear
  D)
   No real roots done clear
  View Solution play_arrow

• question_answer23)
  When are the roots of a quadratic equation real and equal?
  A)
   When the discriminant is positive. done clear
  B)
   When the discriminant is zero. done clear
  C)
   When the discriminant is negative. done clear
  D)
   When the discriminant is non-negative. done clear
  View Solution play_arrow

• question_answer24)
  How are the roots of \[3{{x}^{2}}+7x+8=0\]?
  A)
   Real and unequal done clear
  B)
   Real and equal done clear
  C)
   Not real done clear
  D)
   Cannot be determined. done clear
  View Solution play_arrow

• question_answer25)
  What is the value of 'k' for which the roots of the quadratic equation \[3{{x}^{2}}+2kx+27=0\]are real and equal?
  A)
   9 only                   done clear
  B)
          -9 only done clear
  C)
   9 or-9                   done clear
  D)
          Neither 9 nor-9. done clear
  View Solution play_arrow

• question_answer26)
  Find the sum of the roots of\[{{x}^{2}}+x-210=0\]
  A)
   -2                           done clear
  B)
          29   done clear
  C)
   20                          done clear
  D)
          -1 done clear
  View Solution play_arrow

• question_answer27)
  In the quadratic equation\[9{{x}^{2}}+\alpha x-2=0\], find the value of a for which\[x=\frac{1}{3}\]is its solution.
  A)
   -2                                           done clear
  B)
   3     done clear
  C)
   -4                                           done clear
  D)
   6 done clear
  View Solution play_arrow

• question_answer28)
  The ratio of the length and breadth of a rectangular photo frame is 3 : 2. Find its length if its area is\[\text{864 c}{{\text{m}}^{\text{2}}}\].
  A)
   34 cm   done clear
  B)
          26 cm done clear
  C)
   24 cm   done clear
  D)
          36 cm done clear
  View Solution play_arrow

• question_answer29)
  A two digit number is 4 times the sum of its digits and also 16 more than the product of digits. Find the number.
  A)
   48                          done clear
  B)
          36   done clear
  C)
   44                          done clear
  D)
          32 done clear
  View Solution play_arrow

• question_answer30)
  A quadratic equation\[\alpha {{x}^{2}}+5x+\beta =0\] has two roots\[x=\frac{1}{3}\]and\[x=-2\]. Find the respective values of\[\alpha \]and\[\beta \].
  A)
   3, 2                                        done clear
  B)
   2, -5 done clear
  C)
  -3, 5                       done clear
  D)
          3, -2 done clear
  View Solution play_arrow

• question_answer31)
  Find the common root of the equations\[{{x}^{2}}-7x+10=0\]and\[{{x}^{2}}-10x+16=0\].
  A)
   - 2                          done clear
  B)
          3    done clear
  C)
   5                             done clear
  D)
          2 done clear
  View Solution play_arrow

• question_answer32)
  If the product of the roots of\[{{x}^{2}}-3x+k=10\]is - 2, what is the value of' k'?
  A)
   -2                           done clear
  B)
          8    done clear
  C)
   12                          done clear
  D)
          -8 done clear
  View Solution play_arrow

• question_answer33)
  If \[\text{2}{{\text{a}}^{\text{2}}}+\text{a}-\text{2}=\text{1}\] and a > 0, find 'a'.
  A)
   \[\frac{3}{2}\]                                   done clear
  B)
          1     done clear
  C)
   3                             done clear
  D)
          -1 done clear
  View Solution play_arrow

• question_answer34)
  Find 'a' if\[a-3=\frac{10}{a}\].
  A)
   \[5,-2\]                done clear
  B)
          \[-\sqrt{7},7\] done clear
  C)
   \[\sqrt{7},7\]    done clear
  D)
          \[-5,2\] done clear
  View Solution play_arrow

• question_answer35)
  Find the value of 'p' so that\[{{x}^{2}}+5px+16=0\]has no real root.
  A)
   Greater than\[\frac{8}{5}\] done clear
  B)
   Less than\[\frac{-8}{5}\] done clear
  C)
   Lies between\[\frac{-8}{5}\]and\[\frac{8}{5}\] done clear
  D)
   Less than\[\frac{15}{8}\] done clear
  View Solution play_arrow

• question_answer36)
  Find the value of 'k' for which\[{{x}^{2}}-4x+k=0\]has coincident roots.
  A)
   4                             done clear
  B)
          -4   done clear
  C)
   0                             done clear
  D)
          -2 done clear
  View Solution play_arrow

• question_answer37)
  If the roots of\[{{x}^{2}}+4mx+4{{m}^{2}}+m+1=0\] are real, which of the following is true?
  A)
   \[\text{m}=-\text{1}\]                  done clear
  B)
          \[\text{m}\le -\text{1}\] done clear
  C)
   \[\text{m}\ge -\text{1}\]            done clear
  D)
         \[~\text{m}\ge 0\] done clear
  View Solution play_arrow

• question_answer38)
  What is the ratio of the sum and the product of roots of \[7{{x}^{2}}-12x+18=0\]
  A)
   7 : 12                     done clear
  B)
   2 : 3 done clear
  C)
   3 : 2                       done clear
  D)
          7 : 18 done clear
  View Solution play_arrow

• question_answer39)
  Which of the following is the quadratic equation one of whose roots is\[3-2\sqrt{3}\]?
  A)
   \[{{x}^{2}}+6x-3=0\] done clear
  B)
          \[{{x}^{2}}-6x-3=0\] done clear
  C)
   \[{{x}^{2}}+6x+3=0\] done clear
  D)
          \[{{x}^{2}}-6x+3=0\] done clear
  View Solution play_arrow

• question_answer40)
  If a and R are the roots of the equation \[{{x}^{2}}-8x+p=0\]such that\[{{\alpha }^{2}}+{{\beta }^{2}}=40\], find the value of 'p'.
  A)
   8                             done clear
  B)
          10   done clear
  C)
   12                          done clear
  D)
          14 done clear
  View Solution play_arrow

• question_answer41)
  Which of the following quadratic polynomials can be factorized into a product of real linear factors?
  A)
   \[2{{x}^{2}}-5x+9\]         done clear
  B)
          \[2{{x}^{2}}+4x-5\] done clear
  C)
   \[3{{x}^{2}}+4x+6\]        done clear
  D)
         \[5{{x}^{2}}-3x+2\]   done clear
  View Solution play_arrow

• question_answer42)
  If\[\alpha \]and\[\beta \]are the roots of the equation\[{{x}^{2}}-3x+2=0\], which of the following is the equation whose roots are\[(\alpha +1)\]and\[(\beta +1)\]?
  A)
   \[{{x}^{2}}+5x+6=0\] done clear
  B)
          \[{{x}^{2}}-5x-6=0\] done clear
  C)
   \[{{x}^{2}}-5x-6=0\] done clear
  D)
          \[{{x}^{2}}-5x+6=0\] done clear
  View Solution play_arrow

• question_answer43)
  Which of the following equations has 2 as a root?
  A)
   \[2{{x}^{2}}-7x+6=0\] done clear
  B)
          \[{{x}^{2}}-4x+5=0\] done clear
  C)
   \[3{{x}^{2}}-6x-2=0\] done clear
  D)
          \[{{x}^{2}}+3x-12=0\] done clear
  View Solution play_arrow

• question_answer44)
  If the equation\[ax-5x+c=0\]has 10 as the sum of the roots and also as the product of the roots, which of the following is true?
  A)
   \[\text{a}-\text{c}=\text{5}\]    done clear
  B)
          \[\text{a}=\text{2},\text{c}=\text{3}\] done clear
  C)
   \[~\text{a}=\text{5},\text{ c}=\text{1}\]     done clear
  D)
          \[\text{a}=\text{3},\text{ c}=\text{2}\] done clear
  View Solution play_arrow

• question_answer45)
  Find the product of the roots of the quadratic equation\[~\text{9}{{\text{m}}^{\text{2}}}+\text{24 m}+\text{16}=0\].
  A)
   \[\frac{4}{3}\]                   done clear
  B)
          \[\frac{9}{16}\] done clear
  C)
   \[\frac{16}{9}\]                done clear
  D)
          \[\frac{3}{4}\] done clear
  View Solution play_arrow

• question_answer46)
  What is the nature of the roots of\[3{{x}^{2}}+x+6=0\]?
  A)
   Real and equal done clear
  B)
   Real and distinct done clear
  C)
   Not real done clear
  D)
   Cannot be determined. done clear
  View Solution play_arrow

• question_answer47)
  The perimeter and area of a rectangular park are 80 m and\[~\text{4}00\text{ }{{\text{m}}^{\text{2}}}\]. What is its length?
  A)
   20m                      done clear
  B)
   15m done clear
  C)
   30m      done clear
  D)
          40m done clear
  View Solution play_arrow

• question_answer48)
  If a and P are the roots of the equation\[{{x}^{2}}+kx+12=0\]such that\[\alpha -\beta =1\], what is the value of 'k'?
  A)
  \[0\]                                            done clear
  B)
    \[\pm \text{ }5\] done clear
  C)
    \[\pm \text{ }1\] done clear
  D)
    \[\pm \text{ }7\] done clear
  View Solution play_arrow

• question_answer49)
  What is the value of 'k' for which \[2{{x}^{2}}-kx+k\]has equal roots?
  A)
   4 only                                   done clear
  B)
   0 only done clear
  C)
   8 only                   done clear
  D)
          0, 8 done clear
  View Solution play_arrow

• question_answer50)
  Which of the following statements is true?
  A)
   \[{{x}^{2}}+x+1=0\]has no real roots. done clear
  B)
   \[{{x}^{2}}-4x+3=0\]and\[{{x}^{2}}-x-2=0\]have two common roots. done clear
  C)
   \[{{x}^{2}}-3x-4=0\]have real and equal roots. done clear
  D)
   The roots of\[a{{x}^{2}}+bx+c=0,a\ne 0\]are reciprocal to each other if\[a\ne c\]. done clear
  View Solution play_arrow