Question 1133830
{{{3x^4 -5x^3 - 7x^2 + 3x+2 =0 }}}

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

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

{{{3x^3(x +1)-6x^2(x+1)-2x^2(x+1)+ 4x(x+1)- 3x(x+1)+2(x+1) =0 }}}

{{{(x +1)(3x^3-6x^2-2x^2+ 4x- 3x+2) =0 }}}

{{{(x +1)((3x^3-2x^2)-(6x^2-4x)- (3x-2)) =0 }}}

{{{(x +1)(x^2(3x-2)-2x(3x-2)- (3x-2)) =0 }}}

{{{(x + 1) (3x - 2) (x^2 - 2x - 1) = 0}}}

roots:

if {{{(x + 1)  = 0}}}=>{{{highlight(x=-1)}}}

if {{{ (3x - 2)  = 0}}}=>{{{3x=2}}}=>{{{highlight(x=2/3)}}} (it was given)

if {{{ x^2 - 2x - 1 = 0}}}...use quadratic formula


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

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

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

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

{{{x = (2 +- 2sqrt(2))/2 }}} ...simplify

{{{x = (cross(2)1 +- cross(2)sqrt(2))/cross(2)1 }}}

{{{x = (1 +- sqrt(2)) }}}


=> solutions: 
{{{highlight(x = 1 + sqrt(2)) }}}=> approximately  {{{2.4}}}

or {{{highlight(x = 1 - sqrt(2) )}}}=> approximately {{{-0.4}}}



{{{ graph( 600, 600, -10, 10, -10, 10, 3x^4 -5x^3 - 7x^2 + 3x+2) }}}