How do you find all the zeros of #f(x) = x^3 – 10x^2 + 24x#?

1 Answer
Aug 16, 2016

Answer:

#f(x)# has zeros #0, 4, 6#

Explanation:

#f(x) = x^3-10x^2+24x#

Since all of the terms are divisible by #x#, we can separate that out as a factor. Then we can factor the remaining quadratic using the facts that #4+6=10# and #4*6=24#...

#x^3-10x^2+24x = x(x^2-10x+24) = x(x-4)(x-6)#

Hence zeros:

#x = 0#, #x=4# and #x=6#.