If #1+3i# is a zero of #f#, what are all the zeros of #f(x)=x^4–3x^3+6x^2+2x60#?
1 Answer
Apr 14, 2015
If
There are two ways:

Expand:
#(x(1+3i))(x  (13i))# (factor theorem)
#x^2(1+3i)x(13i)x+10 = x^2  2x + 10# 
Use the sum and product of roots :
#1+3i+1  3i= 2# and#(1+3i)(13i)= 1 + 9 = 10# . Sum is equal to#b/a# , so#b/a=2/1# and#c/a=10/1# . One can solve to find a = 1, b = 2 and c = 10.
Now, for the long division :
FINALLY, we can now factor