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

The quadratic equation p(x) = 0 with real coefficients has purely imaginary roots. Then the equation p(p(x)) = 0 has
  1. Only purely imaginary roots
  2. All real roots
  3. Two real and two purely imaginary roots
  4. Neither real nor purely imaginary roots

Solution

Px=ax2+b with a, b of same sign.
P Px=aax2+b2+b
If x ϵ R or ix ϵ R
⇒   x2  ϵ R
⇒   Pxϵ R
⇒   PPx≠0
Hence real or purely imaginary number can not satisfy P Px=0

Asked in: JEE Advanced 2014 (Paper 2)

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