To find the zeros of the polynomial function f(x) = x³ – 9x² – 20x, we first need to set the function equal to zero:
f(x) = x³ – 9x² – 20x = 0
Next, we can factor the polynomial. First, we notice that each term includes an x, so we can factor x out:
f(x) = x(x² – 9x – 20) = 0
This shows that one of the zeros is x = 0. Now we need to solve the quadratic equation x² – 9x – 20 = 0. We can factor this quadratic as well:
x² – 9x – 20 = (x – 10)(x + 2) = 0
Setting each factor equal to zero gives us the other two zeros:
x – 10 = 0 ⇒ x = 10
x + 2 = 0 ⇒ x = -2
Putting this all together, the zeros of the polynomial function f(x) = x³ – 9x² – 20x are:
- x = 0
- x = 10
- x = -2