How do you find all the zeros of #f(x)=x^3+5x^2+x+5#?

1 Answer
Aug 14, 2016

Answer:

#f(x)# has zeros #-5# and #+-i#

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: #+-i# and #-5#