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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`

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:
D
If quadratric equation has purely imaginary roots, then coefficient of x must be equal to zero.
Let `p(x)=ax^(2)+b` with a, b of same sing and `a, b in R.` Then `p[p(x)=a(ax^(2)+b)^(2)+b`
P(x) has imaginary roots say ix.
Then , also `ax^(2)+b in Rand (ax^(2)+b)^(2)gt0`
`a (ax^(2)+b)^(2)+b ne0, AAx`
Thus, `p[p(x)] ne0, AAx`
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