How do you find all the zeros of #f(x)=x^4 - x^3 - 20x^2#?

1 Answer
Feb 27, 2016

Answer:

Factor #f(x) = x^2(x-5)(x+4)#, hence find zeros:

#x=0# (twice), #x=5# and #x=-4#

Explanation:

Separate out the common factor #x^2# of the terms, then factor the remaining quadratic using #5 xx 4 = 20# and #5 - 4 = 1# as follows:

#f(x) = x^4-x^3-20x^2#

#=x^2(x^2-x-20)#

#=x^2(x-5)(x+4)#

Hence zeros: #x=0# (twice), #x=5# and #x=-4#