Question
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