Find all zeros of the functions

Question

What are all the zeros of these two functions?

x(x-3)²

(x-3)(x+9)³

Answer 1

Hi Michelle, to get the zeros set each factor equal to zero and solve.

x(x-3)²

x=0

x - 3 = 0

x = 3 Because this factor has a power of 2 there are 2 of this zero.

Can write { 0, 3, 3} or 0 multiplicity 1, 3 multiplicity 2

(x-3)(x+9)³

x - 3 = 0

x = 3 multiplicity 1

x + 9 = 0

x = -9 multiplicity 3 (factor has power 3)

{3,-9,-9,-9} or 3 multiplicity 1, -9 multiplicity 3

I hope that helps!

Answer 2

1) x=0, x=3,3

2) x=3, x=-9,-9,-9