Find the zeros of the function f (x) = x^3 + 2x^2 - 25x - 50 = 0

x = - 2, x = - 5, x = + 5

Step-by-step explanation:

x^3 + 2x^2 - 25x - 50 = 0

Factor by grouping

x^3 + 2x^2 - 25x - 50 = 0

x^2 (x+2) - 25 (x+2) = 0

(x+2) (x^2 - 25) = 0

Using the zero product property

x+2 = 0 x^2 - 25 = 0

x=-2 x^2 = 25

x = - 2 Taking the square root of each side

x = ±5