Question

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

Answer 1

Answer:

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