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

Options

A. only purely imaginary roots
B. all real roots
C. two real and two purely imaginary roots
D. neither real nor purealy imaginary roots

Answer

3

Explanation

Since ` p(x) = 0` has purelu imaginary roots,
` p(x) = ax^(2) + c `, where a and c have same sign.
Also , `p(p(x)) = 0 `
`rArr p(x) ` is purely imaginary
`rArr ax^(2) + c ` is purely imaginary
Hence ,x cannot be either purely real or purely imaginary.