10th Class Mathematics Quadratic Equations Question Bank

done Quadratic Equation Total Questions - 40

• question_answer1)
  Identify the quadratic equation from the following.
  A)
   \[m+\frac{1}{m}=1,m\ne 0\]     done clear
  B)
   \[{{m}^{2}}+\frac{1}{m}=1,m\ne 0\] done clear
  C)
   \[{{x}^{2}}-\frac{1}{x}=1,x\ne 0\]      done clear
  D)
   \[{{x}^{2}}+2\sqrt{x}-1=0\] done clear
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• question_answer2)
  If \[{{3.2}^{2x+1}}-{{5.2}^{x+2}}+16=0\] and x is an integer, find the value of x.
  A)
   1 done clear
  B)
   2            done clear
  C)
   3                                 done clear
  D)
   4 done clear
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• question_answer3)
  Which of the following statements is correct?
  A)
   \[x=2\]is a root of \[2{{x}^{2}}+5x+1=0\] done clear
  B)
   \[x=3\] is not a root of \[{{x}^{2}}+3x-5=0\] done clear
  C)
   \[x=-1\] is not a root of \[5{{x}^{2}}-x-1=0\] done clear
  D)
   \[x=-\frac{2}{5}\] is not a root of \[{{x}^{2}}-\frac{8x}{5}-\frac{4}{5}=0\]   done clear
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• question_answer4)
  Maximum value of \[p\left( x \right)=-3{{x}^{2}}+5x-12\] is
  A)
   \[\frac{15}{12}\]                                   done clear
  B)
   \[-9\frac{11}{12}\] done clear
  C)
   \[-\frac{5}{6}\]                         done clear
  D)
   \[\frac{5}{6}\] done clear
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• question_answer5)
  Find the value of ?a? for which \[m=\frac{1}{\sqrt{3}}\] is a root of the equation.\[a{{m}^{2}}+\left( \sqrt{3}-\sqrt{2} \right)m-1=0.\]
  A)
   \[\sqrt{2}\]                                done clear
  B)
   \[2\] done clear
  C)
   \[\sqrt{6}\]        done clear
  D)
   \[5\] done clear
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• question_answer6)
  Which of the following equations has no real roots?
  A)
   \[{{x}^{2}}-4x+3\sqrt{2}=0\] done clear
  B)
   \[{{x}^{2}}+2x-6\sqrt{2}=0\] done clear
  C)
   \[{{x}^{2}}-4x-3\sqrt{2}=0\]   done clear
  D)
  \[3{{x}^{2}}-4\sqrt{3x}-4=0\] done clear
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• question_answer7)
  The sides of two square plots are \[\left( 2x\text{ }-1 \right)m\]and\[\left( 5x+4 \right)m\]. 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)
   50 m                            done clear
  B)
   20 m          done clear
  C)
   26 m                            done clear
  D)
   39 m done clear
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• question_answer8)
  Identify the factors of \[5{{x}^{2}}=4x-\frac{4}{5}\]
  A)
   \[\frac{1}{5},\frac{1}{5}\]                     done clear
  B)
   \[\frac{-3}{2},\frac{3}{2}\] done clear
  C)
   \[\frac{2}{5},\frac{2}{5}\]         done clear
  D)
   \[5,-5\] done clear
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• question_answer9)
  The age of a man is the square of his son's age. One year ago, the man's age was eight times the age of his son. What is the present age of the man?
  A)
   60 years                       done clear
  B)
   49 years    done clear
  C)
   30 years                       done clear
  D)
   40 years done clear
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• question_answer10)
  Following graphs can be drawn to solve the quadratic equation\[4{{x}^{2}}+6x-3=0\]. Choose, the correct method?
  A)
   \[y={{x}^{2}},3x-2y-3=0\] done clear
  B)
   \[y=4{{x}^{2}},6x-2y-3=0\] done clear
  C)
   \[y=3{{x}^{2}},6x-y-3=0\] done clear
  D)
   \[y=2{{x}^{2}},6x+2y-3=0\] done clear
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• question_answer11)
  Find two consecutive even numbers whose product is double that of the greater number.
  A)
   2, 5                              done clear
  B)
   8, 10           done clear
  C)
   2, 4     done clear
  D)
   10, 12 done clear
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• question_answer12)
  Which of the following are the roots of the equation\[{{\left| x \right|}^{2}}+\left| x \right|-12=0\]?

  (i) 1	(ii) - 1
  (iii) 3	(iv) - 3

   
  A)
   Both (i) and (ii) done clear
  B)
   Both (iii) and (iv) done clear
  C)
   (i), (ii), (iii) and (iv)         done clear
  D)
   None of these done clear
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• question_answer13)
  The length and breadth of a rectangle are \[(3k+1)\] cm and \[\left( 2k1 \right)\] cm respectively. Find the perimeter of the rectangle if its area is\[144\text{ }c{{m}^{2}}\].
  A)
   50 cm   done clear
  B)
   20 cm         done clear
  C)
   30 cm              done clear
  D)
   40 cm done clear
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• question_answer14)
  If the roots of the equation \[3a{{x}^{2}}+2bx+c=0\] are in the ratio 2 : 5, then
  A)
   \[8ac=25{{b}^{3}}\]               done clear
  B)
   \[6ac=19{{b}^{2}}\]      done clear
  C)
   \[40{{b}^{2}}=75ac\]        done clear
  D)
   \[8{{b}^{2}}=25ac\] done clear
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• question_answer15)
  The sum of squares of two consecutive positive even integers is 340. Find them.
  A)
   12, 14       done clear
  B)
   4, 6           done clear
  C)
   6, 8                              done clear
  D)
   10, 12 done clear
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• question_answer16)
  Find the relationship between the coefficients of the equation \[r{{x}^{2}}+sx+1=0\], such that \[\alpha :\beta =3:4\] where \[\alpha ,\beta \]are roots of equation.
  A)
   \[12{{s}^{2}}=49rt\]   done clear
  B)
   \[22{{s}^{2}}=-49rt\] done clear
  C)
   \[59{{s}^{2}}=12rt\]               done clear
  D)
   \[59{{t}^{2}}=12rs\] done clear
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• question_answer17)
  If \[\left( {{p}^{2}}-{{q}^{2}} \right){{u}^{2}}+\left( {{q}^{2}}-{{r}^{2}} \right)u+{{r}^{2}}-{{p}^{2}}=0\] and\[\left( {{p}^{2}}-{{q}^{2}} \right){{v}^{2}}+\left( {{r}^{2}}-{{p}^{2}} \right)v+{{q}^{2}}-{{r}^{2}}=0\] have a common root for p, q, r \[\in \] R and u, v being variables in the respective equations, find the common root.
  A)
   ? 3                               done clear
  B)
   1         done clear
  C)
   3                                 done clear
  D)
   ? 6 done clear
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• question_answer18)
  Which of the following are the roots of\[{{\left| y \right|}^{2}}-\left| y \right|-20=0\]?
  A)
   \[4\]                             done clear
  B)
   \[5\]           done clear
  C)
   \[6\]                             done clear
  D)
   \[\pm \,5\] done clear
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• question_answer19)
  Find the value of\[\sqrt{20+\sqrt{20+\sqrt{20+....upto\infty }}}\]
  A)
   5          done clear
  B)
   -4             done clear
  C)
   Either (a) or (b)              done clear
  D)
   6 done clear
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• question_answer20)
  The graphs of\[\frac{1}{2}y={{x}^{2}}\]and\[y=rx+t\]intersect at two points (2, 8) and (6, 72). Find the quadratic equation in x whose roots are \[r+2\] and \[\frac{t}{4}-1\]
  A)
   \[2{{x}^{2}}+6x-123=0\]                   done clear
  B)
   \[3{{x}^{2}}+33x+378=0\] done clear
  C)
   \[{{x}^{2}}-10x-121=0\] done clear
  D)
   \[{{x}^{2}}-11x-126=0\] done clear
  View Solution play_arrow

• question_answer21)
  The equation \[9{{y}^{2}}(m+3)+6(m-3)y+(m+3)=0\], where m is real, has real roots. Which of the following is true?
  A)
   \[m=0\]                        done clear
  B)
   \[m<0\]          done clear
  C)
   \[m\le 0\]      done clear
  D)
   \[m\ge 0\] done clear
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• question_answer22)
  Find the maximum or minimum value of the quadratic expression,\[{{x}^{2}}-5x\text{+}8\], which ever exists.
  A)
   \[y=\frac{1}{2}\]                      done clear
  B)
   \[y=\frac{7}{4}\] done clear
  C)
   \[y=0\]             done clear
  D)
   No solution over real numbers done clear
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• question_answer23)
  Find the roots of the equation\[\frac{1}{x}-\frac{1}{x-a}=\frac{1}{b}-\frac{1}{b-a}\] where \[a\ne 0\].
  A)
   \[{{a}^{3}}-{{b}^{3}}\]and \[(a-b)\]   done clear
  B)
   \[b\]and\[(a-b)\] done clear
  C)
   \[{{a}^{2}}-b\]and \[{{a}^{2}}+b\]   done clear
  D)
   \[a\] and \[b\] done clear
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• question_answer24)
  If the roots of the equation \[2{{x}^{2}}+3x+17=0\] are in the ratio p : q, then find the value of\[\sqrt{\frac{p}{q}}+\sqrt{\frac{q}{p}}.\]
  A)
   \[\frac{\pm 3}{\sqrt{34}}\] done clear
  B)
   \[\pm 3\sqrt{34}\] done clear
  C)
   \[\pm \frac{3\sqrt{6}}{8}\]                     done clear
  D)
   \[\pm 6\sqrt{17}\] done clear
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• question_answer25)
  If the roots of the quadratic equation\[{{x}^{2}}-kx+{{k}^{2}}-3=0\] are real, then the range of the values of k is _________.
  A)
   \[[-2,2]\]            done clear
  B)
   \[[-\infty ,-2]\cup [2,\infty ]\] done clear
  C)
   \[[-3,3]\]                        done clear
  D)
   \[[-\infty ,-3]\cup [3,\infty ]\] done clear
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• question_answer26)
  When is a real number 'a' called the zero of the polynomial f(x)?
  A)
   \[f\left( 0 \right)=a\]       done clear
  B)
   \[f\left( a \right)=f\left( 0 \right)\]       done clear
  C)
   \[f\left( a \right)=0\]                    done clear
  D)
   \[~f\left( \pm a \right)=\pm a\] done clear
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• question_answer27)
  If a 2nd degree equation\[\left( {{b}^{2}}-{{a}^{2}} \right){{x}^{2}}+\left( {{c}^{2}}-{{b}^{2}} \right)x+\left( {{a}^{2}}-{{c}^{2}} \right)=0\]has equal roots, then which of the following conditions will necessarily be true?
  A)
   \[\sum{{{a}^{2}}={{a}^{2}}{{b}^{2}}{{c}^{2}}}\]         done clear
  B)
   \[{{b}^{2}}+{{c}^{2}}={{a}^{2}}\] done clear
  C)
   \[{{b}^{2}}+{{c}^{2}}=2{{a}^{2}}\]        done clear
  D)
   \[{{(a+b+c)}^{2}}=ab+bc+ca\] done clear
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• question_answer28)
  What are the values of x which satisfy the equation\[\sqrt{3x-2}+\frac{1}{\sqrt{3x-2}}=\frac{17}{4}\]?
  A)
   \[6,\frac{11}{16}\]        done clear
  B)
   \[4,\frac{11}{3}\] done clear
  C)
   \[\frac{11}{9},\frac{17}{4}\]                 done clear
  D)
   \[13,\frac{11}{9}\] done clear
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• question_answer29)
  If the roots of the quadratic equation \[a{{x}^{2}}+bx+c=0\]are \[\alpha \] and \[\beta \], then the equation whose roots are \[{{\alpha }^{2}}\] and \[{{\beta }^{2}}\] is
  A)
   \[{{a}^{2}}{{x}^{2}}-\left( {{b}^{2}}-2ac \right)x+{{c}^{2}}=0\] done clear
  B)
   \[\left( {{a}^{2}}-r \right){{x}^{2}}+\left( {{b}^{2}}-r \right)x+{{c}^{2}}r=0\] done clear
  C)
   \[\left( {{a}^{2}}-ac \right){{x}^{2}}+\left( {{b}^{2}}+2ac \right)x+{{c}^{2}}=0\] done clear
  D)
   \[2{{a}^{2}}{{x}^{2}}-\left( {{b}^{2}}+2ac \right)x+2{{c}^{2}}=0\] done clear
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• question_answer30)
  Find the roots of the equation \[{{l}^{2}}\left( {{m}^{2}}-{{n}^{2}} \right){{x}^{2}}+{{m}^{2}}\left( {{n}^{2}}-{{l}^{2}} \right)x+{{n}^{2}}\left( {{l}^{2}}-{{m}^{2}} \right)=0\]
  A)
   \[\frac{{{n}^{2}}\left( {{l}^{2}}-{{m}^{2}} \right)}{{{l}^{2}}\left( {{m}^{2}}-{{n}^{2}} \right)},l\] done clear
  B)
   \[\frac{-{{m}^{2}}\left( {{l}^{2}}-{{m}^{2}}+{{n}^{2}} \right)}{{{l}^{2}}\left( {{m}^{2}}-{{n}^{2}} \right)},\frac{1}{2}\] done clear
  C)
   \[\frac{{{n}^{2}}\left( {{l}^{2}}+{{m}^{2}}+{{n}^{2}} \right)}{{{m}^{2}}\left( {{m}^{2}}-{{n}^{2}} \right)},1\] done clear
  D)
   \[\frac{-{{m}^{2}}\left( {{l}^{2}}+{{n}^{2}} \right)}{mn\left( {{m}^{2}}-{{n}^{2}} \right)},\frac{1}{2}\] done clear
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• question_answer31)
  If \[a-b,b-c\] are the roots of \[a{{x}^{2}}+bx+c=0\], then find the value of \[\frac{(a-b)(b-c)}{2(c-a)}\].
  A)
   \[\frac{b}{c}\]                           done clear
  B)
   \[\frac{c}{2b}\] done clear
  C)
   \[\frac{ab}{c}\]                         done clear
  D)
   \[\frac{bc}{a}\] done clear
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• question_answer32)
  If a and b can take value 1, 2, 5, 6, then the number of the equations of the form \[a{{x}^{2}}+bx+1=0\] having real roots is
  A)
   11                                done clear
  B)
   9      done clear
  C)
   15                                done clear
  D)
   None of these done clear
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• question_answer33)
  If \[\alpha ,\beta \] are the rots of the equation\[a{{x}^{2}}-2bx+c=0\] then \[{{\alpha }^{3}}{{\beta }^{3}}+{{\alpha }^{2}}{{\beta }^{3}}+{{\alpha }^{3}}{{\beta }^{2}}\]
  A)
   \[\frac{-{{c}^{2}}(2b-c)}{{{a}^{3}}}\]           done clear
  B)
   \[\frac{2b{{c}^{3}}}{{{a}^{2}}}\] done clear
  C)
   \[\frac{{{c}^{3}}{{b}^{3}}}{{{a}^{6}}}\]              done clear
  D)
   \[\frac{{{b}^{2}}(2c+3a)}{{{a}^{3}}}\] done clear
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• question_answer34)
  If the product of the roots of\[2{{x}^{2}}-7kx+3{{e}^{3\,\,\log \,\,k}}-1=0\] is 40, then the sum of the roots is
  A)
  \[80\]                             done clear
  B)
   \[\frac{7}{2}\]             done clear
  C)
   \[\frac{21}{2}\]     done clear
  D)
   None of these done clear
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• question_answer35)
  If \[sin\theta ,\text{ }cos\theta \] are roots of the equation\[a{{x}^{2}}-2bx+3c=0\], then
  A)
   \[4{{b}^{2}}-{{a}^{2}}-6ac=0\]       done clear
  B)
   \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}+abc=0\] done clear
  C)
   \[{{a}^{2}}+{{b}^{2}}+2abc-{{c}^{2}}=0\] done clear
  D)
   \[{{a}^{2}}+{{b}^{2}}-2ac=0\] done clear
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• question_answer36)
  tan A, tan B are roots of\[3{{x}^{2}}-5x+6=0\]. then \[si{{n}^{2}}\left( A+B \right)\]
  A)
   \[\frac{14}{15}\]                                   done clear
  B)
   \[\frac{25}{34}\] done clear
  C)
   \[\frac{13}{25}\]                                   done clear
  D)
   \[\frac{11}{46}\] done clear
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• question_answer37)
  If the sum of the roots of \[a{{x}^{2}}+2bx+3c=0\] is equal to the sum of the squares of their reciprocals, then \[9b{{c}^{2}}+2a{{b}^{2}}\]
  A)
   \[18\,abc\]                     done clear
  B)
   \[3{{a}^{2}}c\] done clear
  C)
   \[ab+bc+2ca\]  done clear
  D)
   \[18{{a}^{2}}c+7{{b}^{3}}\] done clear
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• question_answer38)
  Find the value of\[\sqrt{3+\sqrt{3+\sqrt{3+-------}}}\]
  A)
   \[\frac{1\pm \sqrt{13}}{2}\] done clear
  B)
   \[\frac{1\pm \sqrt{3i}}{2}\] done clear
  C)
   \[\frac{1\pm \sqrt{6}}{2}\]                     done clear
  D)
   \[\frac{1\pm \sqrt{3}}{2}\] done clear
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• question_answer39)
    If \[\alpha \] and \[\beta \] are the root of the equation\[2{{x}^{2}}-3x-7=0\] then the value of\[\alpha {{\beta }^{2}}+{{\alpha }^{2}}\beta +\alpha \beta \] are.
  A)
  \[6\]                              done clear
  B)
   \[\frac{-35}{4}\] done clear
  C)
   \[\frac{3}{4}\]                          done clear
  D)
   \[\frac{-15}{8}\] done clear
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• question_answer40)
  Which of the following quadratic equations have equal roots?
  A)
   \[2{{x}^{2}}-3x+5=0\]           done clear
  B)
   \[3{{x}^{2}}-4\sqrt{3x}+4=0\] done clear
  C)
   \[2{{x}^{2}}-6x+3=0\] done clear
  D)
   \[x+\frac{1}{x}=1\] done clear
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