Question

a, b be the root of x² –3x + a = 0 and g, d are the root of

x² –12x + b = 0 and numbers a, b, g, d (in order) form an increasing G.P., then

• A. a = 3, b = 12
• B. a = 12, b = 3
• C. a = 2, b = 32
• D. a = 4, b = 16

Answer 1

Answer: (C)

a = 2, b = 32

Answer 2

x² –3x + a = 0 a, b

x² –12x + b = 0 g, d

a, b, g, d are in G.P. so a, ar, ar², ar³

a + b = 3 = a + ar … (1)

g + d = 12 = ar² + ar³ …. (2)

g² (a + ar) = 12

g² = 4 Ž g = ± 2

Increasing G.P. so r = 2

a + 2a = 3 from (1)

a = 1

a = 1 b = 2

g = 4 d = 8

a = ab b = gd

= 2 b = 32