Question 1133823
{{{x^4 -2x^3 -4x^2+14x-5 =0}}}

{{{x^4+2x^3-x^2 -4x^3-8x^2 +4x+5x^2+10x-5=0 }}}

{{{(x^4+2x^3-x^2) -(4x^3+8x^2 -4x)+(5x^2+10x-5)=0 }}}

{{{x^2(x^2+2x -1) -4x(x^2+2x -1)+5(x^2+2x-1)=0 }}}

 {{{(x^2 + 2 x - 1)(x^2 - 4 x + 5)=0}}}

use quadratic formula:

if {{{x^2 + 2 x - 1=0}}}

{{{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))}}} 

solutions:

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

{{{x = -1 - sqrt( 2)}}} =>approximately {{{-2.4}}}

and

if {{{x^2 - 4 x + 5=0}}}


{{{x = (-(-4) +- sqrt( (-4)^2-4*1*5 ))/(2*1) }}}


{{{x = (4 +- sqrt( 16-20 ))/2 }}} 

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

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

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

solutions:

{{{x = 2 + i }}}

{{{x = 2 - i }}}


{{{ graph( 600, 600, -10, 10, -25, 10, x^4 -2x^3 -4x^2+14x-5) }}}