Find the complex zeros
posted by Ashley on .
Find the complex zeros of the polynomial function. Write f in the factored form. f(x)=x^33x^2+7x5
f(x)=

a little synthetic division shows
f(x) = (x1)(x^22x+5)
And it's easy from there 
First we have to find the real root, (every cubic has at least one real root)
try x = 1 , y = 1  3 + 7  5 = 0 , so x1 is a factor
by synthetic division I got
(x1)(x^2  2x + 5) = 0
So the real zero is when x=1
for complex ...
x^2  2x + 5= 0
x^2  2x = 5
x^2  2x + 15 + 1
(x1)^2 =4
x  1 = ± 2i
x = 1 ± 2i