Posted by **Ashley** on Tuesday, March 26, 2013 at 4:08pm.

Find the complex zeros of the polynomial function. Write f in the factored form. f(x)=x^3-3x^2+7x-5

f(x)=

- Find the complex zeros -
**Steve**, Tuesday, March 26, 2013 at 4:14pm
a little synthetic division shows

f(x) = (x-1)(x^2-2x+5)

And it's easy from there

- Find the complex zeros -
**Reiny**, Tuesday, March 26, 2013 at 4:19pm
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 x-1 is a factor

by synthetic division I got

(x-1)(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 + 1-5 + 1

(x-1)^2 =-4

x - 1 = ± 2i

x = 1 ± 2i

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