Question

Write a polynomial function that meets the stated conditions.The zeros are −2 and 1.

Answer 1

Answer:

A polynomial function that meet those conditions is x² + x - 2 = 0

Step-by-step explanation:

Hi there!

To solve this problem, let´s start writting a generic polynomial function in factored form. Since the function has two zeros, the factored form will have 2 terms:

(x+a)(x+b) = 0

For this equation to be 0, (x+a) or (x+b) have to be zero:

Then:

x + a = 0 ⇒ x = -a

In the same way:

x + b = 0 ⇒ x = -b

Then, the values "a" and "b" are equal to the zeros of the function but with the opposite sign.

In our case:

(x + a)(x + b) = 0

a = the zero of the function with opposite sign, that is, 2

b = -1

Then:

(x + 2)(x - 1) = 0

Apply distributive property:

x² - x + 2x - 2 = 0

x² + x - 2 = 0

Then, a polynomial function that meet those conditions is:

x² + x - 2 = 0