Question 1180426

 {{{mx^2+6x = -m }}}

has no real roots id discriminant {{{b^2-4ac<0}}},  and the parabola it represents does not intersect the x-axis


{{{mx^2+6x +m=0 }}}->{{{a=m}}},{{{b=6}}}, and {{{c=m}}}


{{{b^2-4ac<0}}}...substitute values above

{{{6^2-4m*m<0}}}

{{{36-4m^2<0}}}...simplify, divide by {{{4}}}

{{{9-m^2<0}}}

{{{9<m^2}}}

{{{m>sqrt(9)}}}

{{{m>3}}}  or {{{m<-3}}} 


<a href="https://ibb.co/4mWzD6D"><img src="https://i.ibb.co/4mWzD6D/MSP6789151df94060613145000054begafg338c96da.gif" alt="MSP6789151df94060613145000054begafg338c96da" border="0"></a>


check:

{{{m>3}}}=>{{{m=4}}}

{{{4x^2+6x = -4}}}

{{{ graph( 600, 600, -10, 10, -10, 10, 4x^2+6x +4) }}}


or {{{m<-3}}}=>{{{m=-4}}}

{{{-4x^2+6x = 4}}}

{{{ graph( 600, 600, -10, 10, -10, 10, -4x^2+6x -4) }}}