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Question

If one root of the equation x2+px+q=0 is the square of the other root, then

A
p3+q2q(3p+1)=0
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B
p3+q2+q(1+3p)=0
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C
p3+q2+q(3p1)=0
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D
p3+q2+q(13p)=0
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Solution

The correct option is D p3+q2+q(13p)=0
Let root of the given equation x2+px+q=0 are α and α2

Then, we have αα2=α3=q and α+α2=p

On cubing both sides, we get

α3+(α2)3+3α.α2(α+α2)=p3

q+q2+3q(p)=p3

p3+q2+q(13p)=0

Hence, option D is correct.

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