Question

What are the zeros of the function what are their multiplicities f(x)=5x^3-5x^2-30x

Answer 1

The zeros are x=0,3,-2
There is a multiplicity of 1 for all of them.

Answer 2

To get the zeroes of the equation, we will first need to write the equation in the simplest factorized form as follows:
f(x) = 5x^3 - 5x^2 - 30x
f(x) = 5x (x^2 - x - 6)
f(x) = 5x(x-3)(x+2) ...........> simplest factorized form

Since the function is a multiplication of several terms, this means that for the function to be equal to zero, one of the multiplicands has to be zero.

This means that:
either 5x = 0 .............> This means that x=0
or x-3 = 0 ............> This means that x=3
or x+2 = 0 ...........> This means that x=-2

Based on the above calculations, the zeroes of the function are:
0 , 3 and -2