Question 1134042


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

given: {{{x=-1}}} is a root and {{{x=2/3}}} is a root
if {{{x=2/3}}}=> {{{x-2/3=0}}}
if {{{x=-1}}}=>{{{x+1=0}}}   

{{{x+1=0}}}   and {{{x-2/3=0}}} are factor



{{{3x^4 -5x^3-7x^2+3x+2=0 }}} is divisible by {{{(x + 1)(x -2/3)=x^2 + x/3 - 2/3}}}


.....................({{{3x^2-6x-3}}}
{{{x^2 + x/3 - 2/3}}}|{{{3x^4 -5x^3-7x^2+3x+2 }}}
................................{{{3x^4+x^3-2x^2+3x+2}}}
.........................................{{{-6x^3-2x^2}}}
...........................................{{{-6x^3-2x^2}}}
...............................................       {{{ 0}}}

{{{3x^2-6x-3=0}}} ...simplify
{{{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 }}} 

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

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




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