Question

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

y=(x+1) 2(x-1)(x-2)

Answer 1

Zeros: -1, 1, 2

Explanation:

Hi there!

`y=(x+1)^2(x-1)(x-2)`

The zero-product property states that if two terms, when multiplied, equals 0, one of the terms must be equal to 0.

Therefore, we know that either (x+1), (x-1) or (x-2) is equal to 0:

x+1 = 0

x-1 = 0

x-2 = 0

Now, to solve for the zeros of the function, we can just solve for x:

x+1 = 0 ⇒ x = -1

x-1 = 0 ⇒ x = 1

x-2 = 0 ⇒ x = 2

Notice how for the function, (x+1) is raised to a power of 2. This means that the zero -1 has a multiplicity of 2.

The other zeroes, 1 and 2, have multiplicities of 1.

I hope this helps!