Question 1183785


 

{{{3x^3 + 10x^2 + 7x - 10 = 0}}}.........factor

{{{3x^3 -2x^2+ 12x^2-8x + 15x - 10 = 0}}}

{{{(3x^3 -2x^2)+ (12x^2-8x) + (15x - 10) = 0}}}

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

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


roots:

{{{3x - 2= 0}}}

{{{3x = 2}}}

{{{x=2/3}}}

 {{{x^2 + 4x + 5 = 0}}}....use quadratic formula

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

{{{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)}}} 

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

{{{x=-2-i}}}



an equation each of whose roots are {{{2}}} less than{{{ 3}}} times the roots :

roots are:

{{{x=3*(2/3)-2}}} =>{{{x=0}}}
{{{x=3(-2+i)-2}}}=>{{{ x=-8 + 3i}}}
{{{x=3(-2-i)-2}}} =>{{{x=-8 - 3i}}}


and, equation is:

{{{y=(x-0)(x-(-8 + 3i))(x-(-8 - 3i))}}}

{{{y=x(x+8 - 3i)(x+8 +3i)}}}

{{{y=x(x^2 + 16x + 73)}}}

{{{y=x^3 + 16x^2 + 73x}}}