Determine the zeros of #p(x)=x^3−5x^2−6x# ?

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Answer 1 · 2018-03-20T13:25:04

#x=0#,#x=6# and #x=-1#. See process below

Polinomial Degree= 3. Thus it will have 3 roots or zeroes

#p(x)=x^3-5x^2-6x=x(x^2-5x-6)# (common factor #x#)

In this product we can say that #x=0# because if #x=0#, then #p(x)=0#

Now we have 2 ways to resolve the problem

Method 1: The other factor #x^2-5x-6# we can find the zeroes appliying general formula

#x=(5+-sqrt(25+24))/2=(5+-7)/2# this gives two solutions (roots of equation above) #x=6# and #x=-1#

Method 2: apply Ruffini's algorithm

By the two methods we have: the three roots or zeroes of equation are #x=0#,#x=6# and #x=-1#. For this reason we can factorize #p(x)=(x-6)(x+1)x#