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 $\displaystyle x = 1$ gives a zero!
Hence $\displaystyle (x-1)$ is a factor.
Using long division/synthetic division gives us:
$\displaystyle f(x) = x^4 + 3x^3 - 3x^2 + 3x - 4 = (x-1)(x^3+4x^2+x+4)$
Another root by inspection is $\displaystyle x = -4 $. Again by synthetic/long division we get:
$\displaystyle f(x) = x^4 + 3x^3 - 3x^2 + 3x - 4 = (x-1)(x+4)(x^2+1)$
Now you can find the complex roots in the quadratic!