What are the zeros of the polynomial function f(x) = x³ + x² - 20x?

Solution:

The given polynomial function is

f(x) = x³ + x² - 20x

Taking out x as common

f(x) = x(x² + x - 20)

Now by splitting the middle term

f(x) = x[x² + 5x - 4x - 20]

f(x) = x[x(x + 5) - 4 (x + 5)]

So we get

f(x) = x (x - 4) (x + 5)

Here

x = 0, x - 4 = 0 and x + 5 = 0

x = 0, x = 4 and x = -5.

Therefore, the zeros are 0, 4 and -5.

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What are the zeros of the polynomial function f(x) = x³ + x² - 20x?

Summary:

The zeros of the polynomial function f(x) = x³ + x² - 20x are 0, 4 and -5.