Question 917247
{{{y=-x^3+7x^2-55x+90 }}} factor it first, factor out {{{-1}}}

{{{y=-1(x^3-7x^2+55x-90) }}}............write {{{-7x^2}}} as {{{-2x^2-5x^2}}}  and {{{55x}}} as {{{45x+10x}}}

{{{y=-( x^3-5x^2+45x-2x^2+10x-90)}}} ...group

{{{y=-(( x^3-5x^2+45x)-(2x^2-10x+90)) }}}

{{{y=-(x( x^2-5x+45)-2(x^2-5x+45))}}} 

{{{y=-((x-2)(x^2-5x+45))}}}  ...as you can see one of the factors is {{{x-2}}} and if we set it equal to zero we get: 

{{{x-2=0}}} => {{{x=2}}} which proves that {{{x=2}}} is a real zero of {{{y=-x^3+7x^2-55x+90}}}