Question 1204258
{{{P(x) = x^4 - x^2 + 2x + 2}}}...add {{{2x^3 }}} and {{{-2x^3 }}}, write {{{- x^2}}} as {{{-2x^2+ x^2}}}, and {{{2x }}} as {{{4x -2x}}}

{{{P(x) = x^4 - 2x^3 -2x^2 +2x^3-4x^2+4x + x^2 - 2x + 2}}}....group

{{{P(x) = (x^4 +2x^3+ x^2) - (2x^3+4x^2+2x) +( 2x^2+4x  + 2)}}}

{{{P(x) = x^2(x^2 +2x+ 1) -2x (x^2+2x+1) +2( x^2+2x  + 1)}}}

{{{P(x) = (x^2+2x + 1) (x^2 - 2x + 2)}}}

{{{P(x) = (x + 1)^2 (x^2 - 2 x + 2)}}}


zeros:


{{{0= (x + 1)^2 (x^2 - 2 x + 2)}}}

{{{ (x + 1)^2 =0}}}=> {{{x=-1}}} multiplicity {{{2}}}

{{{x^2 - 2x + 2=0}}} using quadratic formula


{{{x = (-(-2) +- sqrt( (-2)^2-4*1*2 ))/(2*1) }}}

{{{x = (2 +- sqrt( 4-8 ))/2 }}}

{{{x = (2 +- sqrt( -4 ))/2 }}}

{{{x = (2 +- 2i)/2 }}}

{{{x = (1 +- i) }}}

{{{x = 1 + i }}} or {{{x = 1 - i }}}

zeros are:{{{-1}}},{{{-1}}},{{{ 1 + i }}} ,{{{1 - i }}}