Question

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

Answer 1

well if x = 1 is a root then

(x -1) is a factor

multiplicity means that its

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

now distribute the 1st pair of (x -1)s and you get

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

I'll let you finish and check...

hope it helps...

Answer 2

Based on that, I think it's false! Is that correct? @campbell_st

Answer 3

Using @campbell_st 's fine description then multiply out, we get: (x-1)^3=x^3-3 x^2+3 x-1. Compare this to your given equation, if they are equal then answer is True.

Answer 4

well using a little savvy...

the costant term when multiplied out will be -1

and your function has a constant of +1

so it would be false..