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

1 Answer
Aug 11, 2018

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