How do you find all the zeros of #f(x)=x^3+5x^2+x+5#?
1 Answer
Aug 14, 2016
Explanation:
Since the ratio of the first and second terms is the same as that between the third and fourth terms, this cubic will factor by grouping.
So we find:
#x^3+5x^2+x+5#
#=x^2(x+5)+1(x+5)#
#=(x^2+1)(x+5)#
#=(x^2-i^2)(x+5)#
#=(x-i)(x+i)(x+5)#
Hence zeros:
