# Math Help - Real/imaginary zeros

1. ## Real/imaginary zeros

Find all the real imaginary zeros for the polynomial function
f(x) = x^4 + 3x^3 - 3x^2 + 3x - 4.

Thanks for any help!

2. Originally Posted by live_laugh_luv27
Find all the real imaginary zeros for the polynomial function
f(x) = x^4 + 3x^3 - 3x^2 + 3x - 4.

Thanks for any help!
By inspection $x = 1$ gives a zero!

Hence $(x-1)$ is a factor.

Using long division/synthetic division gives us:

$f(x) = x^4 + 3x^3 - 3x^2 + 3x - 4 = (x-1)(x^3+4x^2+x+4)$

Another root by inspection is $x = -4$. Again by synthetic/long division we get:

$f(x) = x^4 + 3x^3 - 3x^2 + 3x - 4 = (x-1)(x+4)(x^2+1)$

Now you can find the complex roots in the quadratic!