Find the zeros of the function. State the multiplicity of multiple zeros.
y=10x^3-10x
To find the zeros of the function y = 10x^3 - 10x, we need to set the function equal to zero and solve for x:
10x^3 - 10x = 0
Factoring out a common factor of 10x:
10x(x^2 - 1) = 0
Setting each factor equal to zero:
10x = 0 or x^2 - 1 = 0
From the first equation, we find that x = 0.
For the second equation, we can factor it as the difference of squares:
(x - 1)(x + 1) = 0
Setting each factor equal to zero:
x - 1 = 0 or x + 1 = 0
From these equations, we find that x = 1 and x = -1.
Therefore, the zeros of the function y = 10x^3 - 10x are x = 0, x = 1, and x = -1.
The multiplicity of each zero in this case is 1.
To find the zeros of the function y = 10x^3 - 10x, we need to set y equal to zero and solve for x.
0 = 10x^3 - 10x
Factoring out 10x, we have:
0 = 10x(x^2 - 1)
Setting each factor equal to zero:
10x = 0 --> x = 0
x^2 - 1 = 0
Using the difference of squares formula, we can factor x^2 - 1 as (x - 1)(x + 1), so:
x - 1 = 0 --> x = 1
x + 1 = 0 --> x = -1
Therefore, the zeros of the function y = 10x^3 - 10x are x = 0, x = 1, and x = -1.
The multiplicity of each zero is 1 since none of them are repeated.