How do you find the zeros of #f(x) = x^3 − 5x^2 − 3x + 15#?

1 Answer
Aug 12, 2016

Answer:

#f(x)# has zeros #+-sqrt(3)# and #5#

Explanation:

#f(x) = x^3-5x^2-3x+15#

Notice that the ratio of the first and second terms is the same as the ratio between the third and fourth terms.

So this cubic will factor by grouping:

#x^3-5x^2-3x+15#

#=(x^3-5x^2)-(3x-15)#

#=x^2(x-5)-3(x-5)#

#=(x^2-3)(x-5)#

#=(x-sqrt(3))(x+sqrt(3))(x-5)#

Hence zeros:

#+-sqrt(3)# and #5#