Question

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

y=12x^3-12x

Answer 1

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

0 = 12x^3 - 12x

Factoring out 12x, we get:

0 = 12x(x^2 - 1)

Setting each factor equal to zero, we have:

12x = 0 or x^2 - 1 = 0

Solving the first equation, we find that x = 0. This is a zero of multiplicity 1.

Solving the second equation, we have:

x^2 = 1

Taking the square root of both sides, we get:

x = 1 or x = -1

Both 1 and -1 are zeros of multiplicity 1.

Therefore, the zeros of the function y = 12x^3 - 12x are x = 0 (multiplicity 1), x = 1 (multiplicity 1), and x = -1 (multiplicity 1).