since α , β be roots of x 2 – 3x + a = 0

∴ α + β = 3, αβ = a

since γ , δ be roots of x 2 – 12x + b = 0

∴ γ + δ = 12, γδ = b

 =

⇒ =

=

16a = b

Let r be the common ratio of α , β , γ , δ

then β = α r, γ = α r 2 and δ = α r 3  α and β be roots of equation x

2 – 3x + a = 0

∴ α + β = α (1 + r) = 3 .........(i)

αβ = α ( α r) = a ..........(ii)

 γ and δ be roots of equation x 2 – 12x + b = 0

∴ γ + δ = α r 2 (1 + r) = 12 ........(iii)

γδ = ( α r 2 ) ( α r 3 ) = b ⇒ α 2 r 5 = b ........(iv)

from (iii) ÷ (i) r 2 = 4 ⇒ r = 2

then from (i), α = 1 ⇒ a = 2

b = 2 5 =32