Question

Find all complex zeros of the polymomial function. Give exact values. List multiple zeroes as necessary.

f(x)x^4+10x^3-31x^2+80x-312

HELP PLEASE

Answer 1

x=3, x=-13 can be found with the rational root theorem and eliminating possible zeroes using linear substitutions (with a lot of work). See http://en.wikipedia.org/wiki/Rational_root_theorem#Example for what I mean by this.
With division you can reduce the polynomial to x^2+8. The roots of this are completely imaginary: +-2sqrt(2)i.