How do you find all the zeros of #f(x)=x^3-x^2+4x-4#?

1 Answer
Aug 14, 2016

Answer:

#f(x)# has zeros #1# and #+-2i#

Explanation:

Note that the ratio of the first and second terms is the same as that between the third and fourth. So this cubic factors by grouping:

#x^3-x^2+4x-4#

#=x^2(x-1)+4(x-1)#

#=(x^2+4)(x-1)#

#=(x^2-(2i)^2)(x-1)#

#=(x-2i)(x+2i)(x-1)#

Hence zeros: #+-2i# and #1#