Final answer:
The zeros of the function f(x) = x² + 5x – 36 are 4 and -9.
Step-by-step explanation:
To find the zeros of the function f(x) = x² + 5x – 36, we need to solve the equation x² + 5x – 36 = 0. We can use factoring, completing the square, or the quadratic formula to find the zeros. Let's use the quadratic formula:
x = (-b ± sqrt(b² - 4ac)) / (2a)
For our equation, a = 1, b = 5, c = -36. Plugging these values into the quadratic formula, we get:
x = (-5 ± sqrt(5² - 4(1)(-36))) / (2(1))
Simplifying further, we have:
x = (-5 ± sqrt(25 + 144)) / 2
x = (-5 ± sqrt(169)) / 2
x = (-5 ± 13) / 2
So, the zeros of the function are x = (-5 + 13) / 2 = 4 and x = (-5 - 13) / 2 = -9.