Question 922226
{{{g(x)=3x^4-13x^3-10x^2+x-5}}} .....write {{{-13x^3}}} as {{{-x^3-12x^3}}}  and 
 {{{-10x^2}}} as {{{x^2+4x^2-15x^2}}}

{{{g(x)=3x^4-x^3+x^2-12x^3+4x^2-4x-15x^2+5x-5}}}  .. group

{{{g(x)=(3x^4-x^3+x^2)-(12x^3-4x^2+4x)-(15x^2-5x+5 ) }}} factor

{{{g(x)=x^2(3x^2-x+1)-4x(3x^2-x+1)-5(3x^2-x+1 )}}} 

{{{g(x)=(x^2-4x-5)(3x^2-x+1)}}}

{{{g(x)=(x^2-5x+x-5)(3x^2-x+1)}}}

{{{g(x)=(x+1)(x-5)(3x^2-x+1)}}}

zeros:

{{{(x+1)(x-5)(3x^2-x+1)=0}}}

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

if {{{(x-5)=0}}}=>{{{x=5}}} ---real solution

{{{3x^2-x+1=0}}}...use quadratic formula

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


{{{x = (-(-1) +- sqrt( (-1)^2-4*3*1 ))/(2*3) }}} 

{{{x = (1 +- sqrt( 1-12 ))/6 }}} 


{{{x = (1 +- sqrt(-11))/6 }}} 


{{{x = (1 +- i*sqrt(11))/6 }}}

complex solutions: {{{x = 1/6 + i*sqrt(11))/6 }}} or {{{x = 1/6 - i*sqrt(11))/6 }}}