If, x4 + 4x3 + 6ax2 + 6bx + c is divisible by x3 + 3x2 + 9x + 3. Then, what is the value of a + b + c?

If, x4 + 4x3 + 6ax2 + 6bx + c is divisible by x3 + 3x2 + 9x + 3. Then, what is the value of a + b + c? Correct Answer 7

Here, f(x) = x4 + 4x3 + 6ax2 + 6bx + c so, let its roots be, α, β, γ, δ and g(x) = x3 + 3x2 + 9x + 3 so, let its roots be, α, β, γ So, from here we can conclude, α + β + γ + δ = -4 and α + β + γ = -3 Thus, δ = -1 This means (x + 1)(x3 + 3x2 + 9x + 3) On solving this equation in simpler form we get, x4 + 4x3 + 12x2 + 12x + 3 => 6a = 12 => a = 2 => 6b = 12 => b = 2 => c = 3 => a + b + c = 7