Question

If α, β be the roots of ax² + bx + c = 0; γ ,δ be the roots of px² + qx + r = 0; and D₁, D₂ the respective discriminants. If α, β, γ, δ are in A.P. then D₁ : D₂ =

• A. $\frac{a^{2}}{b^{2}}$
• B. $\frac{a^{2}}{p^{2}}$
• C. $\frac{b^{2}}{q^{2}}$
• D. $\frac{c^{2}}{r^{2}}$

Answer 1

Answer: (B)

$\frac{a^{2}}{p^{2}}$

Answer 2

Here α – β = γ – δ(As α, β,γ, δ are in A.P.)

⇒(α–β)² = (γ–σ)²

⇒ D₁/a₁² = D₂/a₂² = D₁/D₂ = a₁²/a₂²=a²/p²