Question

Let a₁, b₁ are the roots of x² –6x + p = 0 and a₂, b₂ are the

roots of x² –54 x + q = 0. If a₁, b₁, a₂, b₂ form an increasing

G.P., then the value of (q –p) is-

• A. 440
• B. 540
• C. 640
• D. 340

Answer 1

Answer: (B)

540

Answer 2

Let a₁ = a, b₁ = ar, a₂ = ar², b₂ = ar³

a + ar = 6 …(1)

ar² + ar³ = 54 … (2)

Solving (1) and (2); r = 3 and a = $\frac{3}{2}$

q – p = a²r⁵ – a²r

= a²r (r⁴ –1)

= $\frac{9}{4}$× 3(81 –1) = 540