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Find all real zeros of the function

Find all real zeros of the function-example-1

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Answer:

-1, 0, 1, 6

Explanation:

You want the real zeros of the function g(x) = -3x(x -6)(x² -1).

Special product

The difference of squares is factored as the product of a sum and difference:

a² -b² = (a +b)(a -b)

Factored form

Then the fully-factored function can be written as ...

g(x) = -3x(x -6)(x +1)(x -1)

The zeros are the values of x that make the factors zero:

-3x = 0 ⇒ x = 0

x -6 = 0 ⇒ x = 6

x +1 = 0 ⇒ x = -1

x -1 = 0 ⇒ x = 1

The real zeros of g(x) are -1, 0, 1, 6.

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