Question

If one root of x² + px + q = 0 may be the square of the other, then p^3+q^2 +q=​

Answer 1

Let root of the given equation x

2

+px+q=0 are α and α

2

Then, we have α⋅α

2

=α

3

=q and α+α

2

=−p

On cubing both sides, we get

α

3

+(α

2

)

3

+3α.α

2

(α+α

2

)=−p

3

⇒q+q

2

+3q(−p)=−p

3

⇒p

3

+q

2

+q(1−3p)=0