Hello Surjit,

Let α and β are roots of: x 2 - 6x + a = 0
Let α and γ are roots of: x 2 - cx + 6 = 0
So, α + β = 6 and α.β = a and α + γ = c and α.γ = 6 and β/γ = 4/3
α.β/α.γ = a/6
β/γ = a/6
a = 8

x 2 - 6x + a = 0
x 2 - 6x + 8 = 0
x = 2,6
But α.β = 8
hence α = 2

Answer is 2

Hope this Helps