SOLUTION: F(x)= x^3 - 6x2 +13x - 10 Find all the zeros of the function thx!

Question 248291: F(x)= x^3 - 6x2 +13x - 10
Find all the zeros of the function
thx!
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
x^3 - 6x2 +13x - 10=0
do the rational roots test by dividing +- a/d = +- 10/1
The possible rational factors are +- 10, 5, 2, 1
testing these we find that 2 is a zero.
next we divide x^3 - 6x2 +13x - 10 by x-2 and get x^2-4x+5 which is a quadratic.
x^2-4x+5=0
x^2-4x =-5
x^2-4x+4=-5+4 completing the square.
(x-2)^2=-1
x-2=+-sqrt(-1)
x=2+i, x=2-i the other 2 zeros.
.
Ed
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