Q25 / 60 · JEE Advanced 2014 (Paper 2) · Mathematics

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

A
Only purely imaginary roots
B
All real roots
C
Two real and two purely imaginary roots
Correct answer
D
Neither real nor purely imaginary roots

Solution

P (x) = a x^{2} + b

with a, b of same sign.

P (P (x)) = a {(a x^{2} + b)}^{2} + b

If

x ϵ R o r i x ϵ R

\Rightarrow x^{2} ϵ R

\Rightarrow P (x) ϵ R

\Rightarrow P (P (x)) \neq 0

Hence real or purely imaginary number can not satisfy

P (P (x)) = 0

Hence, the correct answer is option: 'D'.

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