Which of the following are roots of the polynomial function? Check all that apply f (x) = x^3 + 3x^2 - 9x + 5

x = 1 or x = - 5

Step-by-step explanation:

Solve for x:

x^3 + 3 x^2 - 9 x + 5 = 0

The left hand side factors into a product with two terms:

(x - 1) ^2 (x + 5) = 0

Split into two equations:

(x - 1) ^2 = 0 or x + 5 = 0

Take the square root of both sides:

x - 1 = 0 or x + 5 = 0

Add 1 to both sides:

x = 1 or x + 5 = 0

Subtract 5 from both sides:

Answer: x = 1 or x = - 5