To find the zeros of the polynomial function f(x) = x³ + x² – 20x, we need to set the function equal to zero and solve for x:
x³ + x² – 20x = 0
We can factor out the common term, which in this case is x:
x(x² + x – 20) = 0
The first factor gives us one zero:
- x = 0
Now, we need to solve the quadratic equation x² + x – 20 = 0. We can factor this quadratic:
(x + 5)(x – 4) = 0
This gives us two additional zeros:
- x = -5
- x = 4
In summary, the zeros of the polynomial function are:
- x = 0
- x = -5
- x = 4