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Question: If one roots is square of the other root of the equation x<sup>2</sup> + px + q = 0, then the relati...

If one roots is square of the other root of the equation x2 + px + q = 0, then the relation between p and q is

A

p3 – q(3p – 1) + q2 = 0

B

p3 – q(3p + 1) + q2 = 0

C

p3 + q(3p – 1) + q2 = 0

D

p3 + q(3p + 1) + q2 = 0

Answer

p3 – q(3p – 1) + q2 = 0

Explanation

Solution

x2 + px + q = 0

Roots are α and α

⇒ α + α2 = - p, αα2 = 1 ⇒ α = q1/3

∴ (q)1/3 + (q1/3)2 = - p

Taking cube of both sides

q + q2 + 3q (a1/3 + q2/3) = - p3

⇒ q + q2 – 3pq = - p3 ⇒ p3 + q2 – q(3p – 1)= 0