Write a polynomial function that meets the stated conditions. the zeros are −1, 2, and 7.

A polynomial function that meet the conditions is x³ - 8x² + 5x + 14 = 0

Step-by-step explanation:

Hi there!

Let´s start writting a generic factored function. In this case, the function has 3 zeros so that the factored form will have 3 terms:

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

For this expression to be 0, either (x+a) = 0 or (x+b) = 0 or (x+c) = 0

Then:

x + a = 0 ⇒ x = -a

x + b = 0 ⇒ x = -b

x + c = 0 ⇒ x = -c

Then, the values "a", "b" and "c" are equal to the zeros of the function but with opposite sign. Then, in our case:

a = 1

b = -2

c = -7

Then, the polynomial fuction will be:

(x + 1)(x - 2)(x - 7) = 0

Apply distributive property:

(x² - 2x + x -2)(x -7) = 0

(x² - x - 2)(x - 7)

x³ - x² - 2x - 7x² + 7x + 14 = 0

x³ - 8x² + 5x + 14 = 0

Then, a polynomial function that meets the conditions is:

x³ - 8x² + 5x + 14 = 0

Have a nice day!