Question

The cubic equation whose roots are the AM, GM and HM of the roots of x2 - 2px + q2 = 0 is

• A. (A) (x - p)(x - q)(x - p - q) = 0
• B. (B) (x - p)(x - |q|)(px - q2) = 0
• C. (C) x3−(p+|q|+q2p)x2+(p|q|+q2+|q|3p)x−|q|3=0
• D. (D) None of these

Answer 1

Answer: (B), (C)

(B) (x - p)(x - |q|)(px - q2) = 0

Answer 2

Explanation:
α+β=2p,αβ=q2∴AM of roots =p,GM of roots =|q|,HM of roots =2αβα+β=2q22p∴ The cubic equation is (x−p)(x−|q|)(x−q2p)=0