How do you find all zeros with multiplicities of #f(x)=9x^3-5x^2-x#?

1 Answer
Aug 11, 2018

Answer:

#x=0" "# or #" "x = 5/18+-sqrt(61)/18#

all with multiplicity #1#

Explanation:

#0 = 36f(x)#

#color(white)(0) = 36(9x^3-5x^2-x)#

#color(white)(0) = x(324x^2-180x-36)#

#color(white)(0) = x((18x)^2-2(18x)(5)+25-61)#

#color(white)(0) = x((18x-5)^2-(sqrt(61))^2)#

#color(white)(0) = x(18x-5-sqrt(61))(18x-5+sqrt(61))#

Hence:

#x=0#

or:

#18x=5+-sqrt(61)" "# so #" "x = 5/18+-sqrt(61)/18#