2024 · Q10
Suppose p(x) = x⁴ + a₃x³ + a₂x² + a₁x + a₀ and q(x) = x⁴ + b₃x³ + b₂x² + b₁x + b₀ polynomials. If α, β, γ, δ are zeros of p(x) and α, β, γ, λ are zeros of q(x), then what is (p(x)-q(x))/((x-α)(x-β)(x-γ)) equal to ?
Elementary MathematicsAlgebra
- A- λ + δ
- Bλ - δ
- Cλ + δ
- D- λ - δ
Explanation
p(x) − q(x) = (x − α)(x − β)(x − γ)[(x − δ) − (x − λ)] = (x − α)(x − β)(x − γ)(λ − δ). Dividing by (x − α)(x − β)(x − γ) leaves the constant λ − δ. Hence the quotient is option (b).