Find the zeros of the function. State the multiplicity of multiple zeros.

y=6x^3-6x

1 answer

To find the zeros of the function, we set y equal to zero and solve for x:

0 = 6x^3 - 6x

Next, we can factor out a common factor of 6x from both terms:

0 = 6x(x^2 - 1)

Now, we have two factors: 6x and (x^2 - 1).

Setting each factor equal to zero, we have:

6x = 0 --> x = 0

x^2 - 1 = 0

Using the difference of squares formula, we have:

(x - 1)(x + 1) = 0

Setting each factor equal to zero, we have:

x - 1 = 0 --> x = 1

x + 1 = 0 --> x = -1

Therefore, the zeros of the function are: x = 0, x = 1, and x = -1.

The multiplicity of each zero is 1, meaning each zero appears only once in the factored form of the function.