Question 134217

{{{f(x)=x^3-6x^2+9x}}} Start with the given equation



{{{0=x^3-6x^2+9x}}} Set f(x) equal to zero



{{{0=x(x^2-6x+9)}}} Factor out an "x"



{{{0=x(x-3)(x-3)}}} Factor {{{x^2-6x+9}}} to get {{{(x-3)(x-3)}}} (note: if you need help with factoring, check out this <a href=http://www.algebra.com/algebra/homework/playground/change-this-name4450.solver>solver</a>)




Now set each factor equal to zero:

{{{x=0}}}, {{{x-3=0}}} or {{{x-3=0}}}


{{{x=0}}}, {{{x=3}}} or {{{x=3}}}   Now solve for x in each case




------------


Answer:


So our solutions are 


{{{x=0}}} or {{{x=3}}}





Notice if we graph {{{y=x^3-6x^2+9x}}}  we can see that the roots are {{{x=0}}} and  {{{x=3}}} . So this visually verifies our answer.



{{{ graph(500,500,-10,10,-10,10,0, x^3-6x^2+9x) }}}