Question 802709


{{{-x^3 + 5x^2 - 11x + 55 = 0 }}}.....factor, group first two terms together and second two terms together

{{{-(x^3 -5x^2) - (11x - 55) = 0 }}}....factor out {{{x^2}}} from the first group and {{{11}}} from the second group

{{{-x^2(x-5) - 11(x -5) = 0 }}}

{{{(x-5) -(x^2+11 ) = 0 }}}....use zero product rule to find roots

if {{{(x-5)  = 0 }}}=> {{{x=5}}}.....one real root

if {{{  -(x^2+11 ) = 0 }}} => {{{x^2=-11}}}=> {{{x=sqrt(-11)}}}=>{{{x=i*sqrt(11)}}} or {{{x=-i*sqrt(11)}}}

so, you have one real root {{{x=5}}}, and two complex roots {{{x=i*sqrt(11)}}} and {{{x=-i*sqrt(11)}}}

{{{ graph( 600,600, -10, 10, -10, 60,-x^3 + 5x^2 - 11x + 55) }}}