f(x)=x(2x-5)(x-5) find all zeros

Question

It said to find all zeros but i don't know where to start

Answer 1

Since f(x) is factored (quite conveniently), just set each factor equal to zero and solve for x.  There are 3 zeros: x₁, x₂, and x₃.

 

x₁ = 0

 

2x₂ - 5 = 0 ⇒ x₂ = 5/2

 

x₃ - 5 = 0 ⇒ x₃ = 5