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JEE Advanced 2014Paper 2
Exam
JEE Advanced
Year
2014
Paper
Paper 2
Subject
Mathematics
Chapter
Quadratic Equation

JEE Advanced 2014 · Paper 2 · Mathematics · Quadratic Equation

The quadratic equation p ( x ) = 0 with real coefficients has...

The quadratic equation p(x)=0p ( x ) = 0 with real coefficients has purely imaginary roots. Then the equation p(p(x))=0p ( p ( x ) ) = 0 has

Options

  1. AOnly purely imaginary roots
  2. BAll real roots
  3. CTwo real and two purely imaginary roots
  4. DNeither real nor purely imaginary roots

Correct answer

D. Neither real nor purely imaginary roots

Step-by-step solution

P(x)=ax2+bP\left(x\right) = a{x}^{2} + b with a, b of same sign.
P(P(x))=a(ax2+b)2+bP\left(P\left(x\right)\right) = a{\left(a{x}^{2} + b\right)}^{2} + b
If xϵRorixϵRxϵRorixϵR
⇒x2ϵR⇒ {x}^{2}ϵR
⇒P(x)ϵR⇒ P\left(x\right)ϵR
⇒P(P(x))≠0⇒ P\left(P\left(x\right)\right) \ne 0
Hence real or purely imaginary number can not satisfy P(P(x))=0P\left(P\left(x\right)\right) = 0
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