Question 481249

{{{x^3-5x=0}}}


{{{x^3-5x=0}}}.......factor it out


{{{x(x^2-5)=0}}}...now you have a product of {{{x}}} and {{{(x^2-5)}}} equal to {{{0}}}

means if {{{x=0}}}, whole product is equal to {{{0}}}...that is first solution

and, if {{{x^2-5=0}}}, whole product is equal to {{{0}}}; so, find other two solutions

solve {{{x^2-5=0}}} for {{{x}}}

{{{x^2-5=0}}}...->...{{{x^2=5}}}....->...{{{x}}}=+-{{{sqrt(5)}}}

finally, roots are:

{{{x=0}}}

{{{x=sqrt(5)}}} or {{{x=1.5}}}

{{{x=-sqrt(5)}}} or {{{x=-1.5}}}