Find a polynomial f (x) of degree 4 that has the following zeros.

4,9,0,-1

Leave your answers in factored form.

The answer to your question is (x₁ - 4) (x₂ - 9) (x₃) (x₄ + 4)

Step-by-step explanation:

Data

zeros of a polynomial = 4, 9, 0, - 1

Process

1. - Equal each root to zero

x₁ = 4 x₂ = 9 x₃ = 0 x₄ = - 1

x₁ - 4 = 0 x₂ - 9 = 0 x₃ = 0 x₄ + 1 = 0

2. - Write the terms together

(x₁ - 4) (x₂ - 9) (x₃) (x₄ + 4)

3. - Expand to check the answer

(x - 4) (x - 9) = x² - 13x + 36

(x² - 13x + 36) (x) = x³ - 13x² + 36x

(x³ - 13x² + 36x) (x + 4) = x⁴ - 13x³ + 36x² + 4x³ - 52x² + 144x

= x⁴ - 9x³ - 16x² + 144