Question

The root x = 1 has multiplicity 3 for the function f(x)=x^3-x^2-x+1. True or false

Answer 1

x^3 - x^2 - x + 1 = 0
Plug in x = 1:-
1 -1 - 1 + 1 = 2 - 2 = 0 so x =1 is a root.

If it has multiplicity 3 then the function will factor to (x - 1)^3:-

(x - 1)^3 = (x - 1)(x^2 - 2x + 1) = x^3 - 2x^2 + x - x^2 + 2x - 1

= x^3 - 3x^2 + 3x - 1 so it is FALSE