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If one root is square of the other root ...

If one root is square of the other root of the equation `x^2+p x+q=0` then the relation between p and q is

A

`p^(3)-q(3p-1)+q^(2)=0`

B

`p^(3)-q(3p+1)+q^(2)=0`

C

`p^(3)+q(3p-1)+q^(2)=0`

D

`p^(3)+q(3p+1)+q^(2)=0`

Text Solution

Verified by Experts

The correct Answer is:
A
Let the roots of `x^(2)+px+q=0` be `alphaand alpha^(2).`
`impliesalpha+alpha^(2)=-pand alpha^(3)=q`
`impliesalpha(alpha+1)=-p`
`impliesalpha^(3){alpha^(3)+1+3alpha(alpha+1)}=-p^(3)["cubing both sides"]`
`impliesq(q+1-3p)=-p^(3)`
`impliesp^(3)-(3p-1)q+q^(2)=0`
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