JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank

done Solution of quadratic inequations and Miscellaneous equations Total Questions - 20

• question_answer1)
  The number of real values of x for which the equality \[\left| \,3{{x}^{2}}+12x+6\, \right|=5x+16\] holds good is [AMU 1999]
  A)
  4 done clear
  B)
  3 done clear
  C)
  2 done clear
  D)
  1 done clear
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• question_answer2)
  If x is real and satisfies \[x+2>\sqrt{x+4},\] then [AMU 1999]
  A)
  \[x<-2\] done clear
  B)
  \[x>0\] done clear
  C)
  \[-3<x<0\] done clear
  D)
  \[-3<x<4\] done clear
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• question_answer3)
  The complete solution of the inequation \[{{x}^{2}}-4x<12\,\text{ is}\] [AMU 1999]
  A)
  \[x<-\,2\] or \[x>6\] done clear
  B)
  \[-\,6<x<2\] done clear
  C)
  \[2<x<6\] done clear
  D)
  \[-\,2<x<6\] done clear
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• question_answer4)
  The number of roots of the equation \[\log (-2x)\] \[=2\log (x+1)\] are [AMU 2001]
  A)
  3 done clear
  B)
  2 done clear
  C)
  1 done clear
  D)
  None of these done clear
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• question_answer5)
  The set of all real numbers x for which \[{{x}^{2}}-|x+2|+x>0,\] is [IIT Screening 2002]
  A)
  \[(-\infty ,\,\,-2)\,\cup (2,\,\infty )\] done clear
  B)
  \[(-\infty ,\,\,-\sqrt{2})\,\cup (\sqrt{2},\,\infty )\] done clear
  C)
  \[(-\infty ,\,\,-1)\,\cup (1,\,\infty )\] done clear
  D)
  \[(\sqrt{2},\,\infty )\] done clear
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• question_answer6)
  If \[{{x}^{2}}+2ax+10-3a>0\] for all \[x\in R\], then  [IIT Screening 2004]
  A)
  \[-5<a<2\] done clear
  B)
  \[a<-5\] done clear
  C)
  \[a>5\] done clear
  D)
  \[2<a<5\] done clear
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• question_answer7)
  The roots of the equation \[{{x}^{4}}-4{{x}^{3}}+6{{x}^{2}}-4x+1=0\] are  [MP PET 1986]
  A)
  1, 1, 1, 1 done clear
  B)
  2, 2, 2, 2 done clear
  C)
  3, 1, 3, 1 done clear
  D)
  1, 2, 1, 2 done clear
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• question_answer8)
  If the roots of the equation \[8{{x}^{3}}-14{{x}^{2}}+7x-1=0\] are in G.P., then the roots are  [MP PET 1986]
  A)
  \[1,\frac{1}{2},\frac{1}{4}\] done clear
  B)
  2, 4, 8 done clear
  C)
  3, 6, 12 done clear
  D)
  None of these done clear
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• question_answer9)
  If the sum of the two roots of the equation \[4{{x}^{3}}+16{{x}^{2}}-9x-36=0\] is zero, then the roots are  [MP PET 1986]
  A)
  1, 2 -2 done clear
  B)
  \[-2,\frac{2}{3},-\frac{2}{3}\] done clear
  C)
  \[-3,\frac{3}{2},-\frac{3}{2}\] done clear
  D)
  \[-4,\frac{3}{2},-\frac{3}{2}\] done clear
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• question_answer10)
  One root of the following given equation \[2{{x}^{5}}-14{{x}^{4}}+31{{x}^{3}}-64{{x}^{2}}+19x+130=0\] is  [MP PET 1985]
  A)
  1 done clear
  B)
  3 done clear
  C)
  5 done clear
  D)
  7 done clear
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• question_answer11)
  If two roots of the equation \[{{x}^{3}}-3x+2=0\] are same, then the roots will be [MP PET 1985]
  A)
  2, 2, 3 done clear
  B)
  1, 1, -2 done clear
  C)
  - 2, 3, 3 done clear
  D)
  -2, -2, 1 done clear
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• question_answer12)
  If \[a,b,c\] are real and \[{{x}^{3}}-3{{b}^{2}}x+2{{c}^{3}}\] is divisible by \[x-a\] and\[x-b\], then
  A)
  \[a=-b=-c\] done clear
  B)
  \[a=2b=2c\] done clear
  C)
  \[a=b=c\],\[a=-2b=-2c\] done clear
  D)
  None of these done clear
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• question_answer13)
  If  a, b and g  are the roots of \[{{x}^{3}}+8=0\], then the equation whose roots are \[{{\alpha }^{2}},{{\beta }^{2}}\]and \[{{\gamma }^{2}}\]is
  A)
  \[{{x}^{3}}-8=0\] done clear
  B)
  \[{{x}^{3}}-16=0\] done clear
  C)
  \[{{x}^{3}}+64=0\] done clear
  D)
  \[{{x}^{3}}-64=0\] done clear
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• question_answer14)
  If \[\alpha ,\,\beta ,\,\gamma \] are the roots of the equation \[{{x}^{3}}+4x+1=0,\] then \[{{(\alpha +\beta )}^{-1}}+{{(\beta +\gamma )}^{-1}}+{{(\gamma +\alpha )}^{-1}}=\] [EAMCET 2003]
  A)
  2 done clear
  B)
  3 done clear
  C)
  4 done clear
  D)
  5 done clear
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• question_answer15)
  If the sum of two of the roots of \[{{x}^{3}}+p{{x}^{2}}+qx+r=0\] is zero, then pq = [EAMCET 2003]
  A)
  - r done clear
  B)
  r done clear
  C)
  2 r done clear
  D)
  - 2 r done clear
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• question_answer16)
  If \[\alpha ,\beta ,\gamma \]are the roots of the equation \[{{x}^{3}}+x+1=0\], then the value of \[{{\alpha }^{3}}{{\beta }^{3}}{{\gamma }^{3}}\] [MP PET 2004]
  A)
  0 done clear
  B)
  - 3 done clear
  C)
  3 done clear
  D)
  - 1 done clear
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• question_answer17)
  The roots of the equation \[{{x}^{4}}-2{{x}^{3}}+x=380\] are [UPSEAT 2004]
  A)
  \[5,-4,\frac{1\pm 5\sqrt{-3}}{2}\] done clear
  B)
  \[-5,4,-\frac{1\pm 5\sqrt{-}3}{2}\] done clear
  C)
  \[5,4,\frac{-1\pm 5\sqrt{-}3}{2}\] done clear
  D)
  \[-5,-4,\frac{1\pm 5\sqrt{-}3}{2}\] done clear
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• question_answer18)
  If a, b and g are the roots of equation \[{{x}^{3}}-3{{x}^{2}}+x+5=0\] then \[y=\sum {{\alpha }^{2}}+\alpha \beta \gamma \] satisfies the equation  [J & K 2005]
  A)
  \[{{y}^{3}}+y+2=0\] done clear
  B)
  \[{{y}^{3}}-{{y}^{2}}-y-2=0\] done clear
  C)
  \[{{y}^{3}}+3{{y}^{2}}-y-3=0\] done clear
  D)
  \[{{y}^{3}}+4{{y}^{2}}+5y+20=0\] done clear
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• question_answer19)
  If a, b, g are the roots of the equation \[2{{x}^{3}}-3{{x}^{2}}+6x+1=0\], then \[{{\alpha }^{2}}+{{\beta }^{2}}+{{\gamma }^{2}}\] is equal to [Karnataka CET 2005]
  A)
  -\[\frac{15}{4}\] done clear
  B)
  \[\frac{15}{4}\] done clear
  C)
  \[\frac{9}{4}\] done clear
  D)
  4 done clear
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• question_answer20)
  The solution set of the equation \[pq{{x}^{2}}-{{(p+q)}^{2}}x+{{(p+q)}^{2}}=0\]  is [Kerala (Engg.) 2005]
  A)
  \[\left\{ \frac{p}{q},\,\frac{q}{p} \right\}\] done clear
  B)
  \[\left\{ pq,\,\frac{p}{q} \right\}\] done clear
  C)
  \[\left\{ \frac{q}{p},\,pq \right\}\] done clear
  D)
  \[\left\{ \frac{p+q}{p},\,\frac{p+q}{q} \right\}\] done clear
  E)
  \[\left\{ \frac{p-q}{p},\,\frac{p-q}{q} \right\}\] done clear
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