Question 1133833

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

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

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

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

solutions:

if {{{(2 x + 1) = 0}}} =>{{{2x=-1}}}=>{{{x=-1/2}}}

if {{{ (x^2 + x + 2) = 0}}}

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

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

{{{x = (-1 +- sqrt( 1-8 ))/2 }}} 

{{{x = (-1 +- sqrt( -7 ))/2 }}} 

{{{x = (-1 +- sqrt(-1)*sqrt(7 ))/2 }}} 

{{{x = (-1 +- i*sqrt(7 ))/2 }}} 


=>{{{x = (-1 + i*sqrt(7 ))/2 }}}  or {{{x = (-1 - i*sqrt(7 ))/2 }}}




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