Question

Determine the zeros and state the multiplicity of any repeated zeros for f(x)=3x(x+2)^2(2x-1)^3

Answer 1

see explanation

Explanation:

To determine the zeros of f(x) equate f(x) = 0, that is

3x(x + 2)²(2x - 1)³ = 0

Equate each factor to zero and solve for x

3x = 0 ⇒ x = 0 with multiplicity 1

(x + 2)² = 0 ⇒ x = - 2 with multiplicity 2

(2x - 1)³ = 0 ⇒ x =
`(1)/(2)` with multiplicity 3