Question

What are the zeros of the function?

f(x)= x³ + x² - 6x
O-3, 0, and 1
O-1, 0, and 3
O
-3, 0, and 2
-2, 0, and 3

Answer 1

-3, 0, and 2

Explanation:

x^3 + x^2 - 6x = 0

x(x^2 + x - 6) = 0

From this, we can see that one of the two terms has to be 0 for the entire thing to be 0 since they are being multiplied together. So, one solution is x = 0. Let's explore the other solution, where the second term is 0.

x^2 + x - 6 = 0

(x - 2)(x + 3) = 0

Again, one of these two terms has to be equal to 0. Let's explore both options.

x - 2 = 0

x = 2

x + 3 = 0

x = -3