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