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

The quadratic equation `p(x)=0` with real coefficients has purely imaginary roots. Then the equation `p(p(x))=0` has only purely imaginary roots at real roots two real and purely imaginary roots neither real nor purely imaginary roots

A

only purely imaginary roots

B

all real roots

C

two real and two purely imaginary roots

D

neither real nor purely imaginary roots

Text Solution

Verified by Experts

The correct Answer is:
A, D
Sicne `b=0` for `p(x)=ax^(2)+bx+c` as roots are pure imaginary.
`impliesx=+-sqrt((-c+-isqrt(c)))/a)`, which are clearly neigher pure real nor pure imaginary as `c!=0`
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