SOLUTION: I want to make sure i am doing this correctly... Question is: Determine ALL REAL ZEROS (and multiplicities for them) for the following polynomial functions. f(x)=x^4-6x^3+13x^2

Question 61368: I want to make sure i am doing this correctly... Question is: Determine ALL REAL ZEROS (and multiplicities for them) for the following polynomial functions.
f(x)=x^4-6x^3+13x^2-24x+36
I went to the tutor here at school, and it seemed like the kid did not know what the correct answer would be... I have..
Real Zeros= x=3
but i don't think i am right.. Please help.. Thanks again..

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
ALL REAL ZEROS (and multiplicities for them) for the following polynomial functions.
f(x)=x^4-6x^3+13x^2-24x+36
Yes, 3 is a zero of multiplicity 2.
So you have factors of (x-3)^2 and (x^2+4)
If x^2+4=0 x=2i or x=-2i
ZEROES:
x=3 with multiplicity 2
x=2i with multiplicity 1
x=-2i with multiplicity 1
Cheers,
Stan H.

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