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

Solution:

Given, f(x) =  x³ - x² - 20x

We have to find the zero of the polynomial function.

On solving,

f(x) =  x³ - x² - 20x

Taking out x,

x(x² - x - 20) = 0

By splitting the middle term

x(x² - 5x + 4x - 20) = 0

Taking out the common terms

x(x(x - 5) + 4(x - 5)) = 0

x(x + 4)(x - 5) = 0

So, x = 0

x + 4 = 0

x = -4

x - 5 = 0

x = 5

Therefore, the zeros of the polynomial function 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.