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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 purealy imaginary roots

Text Solution

Verified by Experts

The correct Answer is:
3
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.
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