Question 1134151


{{{x^4-3x^3-2x^2+10x-12=0 }}}...write {{{-3x^3}}} as {{{-2x^3-x^3}}}, {{{ -2x^2}}} as {{{2x^2+2x^2-6x^2}}} and {{{10x}}} as {{{-2x+12x}}}

{{{x^4-2x^3+2x^2-x^3+2x^2-2x-6x^2+12x-12=0}}}...group

{{{(x^4-2x^3+2x^2)-(x^3-2x^2+2x)-(6x^2-12x+12)=0}}}..factor

{{{x^2(x^2-2x +2 )-x(x^2-2x+2)-6(x^2-2x+2)=0}}}

{{{(x^2 - x - 6) (x^2 - 2x + 2) = 0}}}

{{{(x^2+2x - 3x - 6) (x^2 - 2x + 2) = 0}}}

{{{((x^2+2x) -( 3x + 6)) (x^2 - 2x + 2) = 0}}}

{{{(x(x+2) -3( x + 2)) (x^2 - 2x + 2) = 0}}}

{{{(x - 3) (x + 2) (x^2 - 2 x + 2) = 0}}}


=> two solutions are: {{{highlight(x  = 3)}}} and {{{highlight(x  = -2)}}}

next two solutions find using quadratic formula for

{{{x^2 - 2 x + 2 = 0}}}

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 


{{{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) }}} 

solutions: {{{highlight(x = 1 + i) }}} or {{{highlight(x = 1 - i) }}}