Question

If α, β are the roots of the equation ax² + bx + c = 0 and α′, β′ those of a′ x² + b′ x + c′ = 0 and the circle having A(α, α′) and B(β, β′) as diameter passes  through the origin, and the point  (b/a,b'/a')

(A) a′c + ac′ = 0 

(B) a′b ± ab′ = 0 

(C) b′c + bc′ = 0 

(D) a² b′ 2 + a′ 2 b² = 0

Answer 1

Correct option (A,D)

Explanation:

We have α+β = –b/a, αβ = c/a, α′+β′ = –b′/a′ and α′β′ = c′/a′. 

 Therefore, equation of the circle having AB as diameter is

Since it passes through the origin, a′ c + ac′ = 0 and through (b/a, b′/a′)