I'm working with finding roots of polynomial equations with degrees of 3 or higher. I have the equation

Question

r(x)=x^4-6x^3+12x^2=6x-13

I used a graphing calculator to find the real roots of 1,-1

Then I did synthetic using -1, and I ended up with the equation

x^3-6x^2+2x-13

How do I get this to a quadratic so that I can find the imaginary roots? A friend suggested grouping, but I'm not real good at grouping, and I couldn't figure out how to factor it or group it. Any help would be appreciated.

Thanks,
Josh

Answer 1

*in the original equation it was supposed to be +6x-13 not =6x-13

Answer 2

3 < b + a X 7