<PRE><B>Question 1085127</B>



 {{{6x^2 + 6x + k =0}}}-&gt;{{{a=6}}}, {{{b=6}}}, and{{{ c=k}}}

if the discriminant {{{b^2-4ac&gt;0}}}, the equation has two distinct real roots

{{{6^2-4*6k&gt;0}}}

{{{36-24k&gt;0}}}

{{{36&gt;24k}}}

{{{k&lt;36/24}}}

{{{k&lt;6/4}}}

{{{k&lt;3/2}}}

{{{k&lt;1.5}}}

so, we can try {{{k=1}}} which is less than {{{k&lt;1.5}}}

{{{6x^2 + 6x + 1 =0}}}

{{{ graph( 600, 600, -10, 10, -10, 10, 6x^2 + 6x + 1) }}} 



if the discriminant{{{ b^2-4ac=0}}}, the equation has two equal real roots

{{{6^2-4*6k=0}}}

{{{36-24k=0}}}

{{{36=24k}}}

{{{k=36/24}}}

{{{k=6/4}}}

{{{k=3/2}}}

{{{k=1.5}}}

{{{ graph( 600, 600, -10, 10, -10, 10, 6x^2 + 6x + 1.5) }}}


if the discriminant {{{b^2-4ac&lt;0}}}, there are no real solutions

{{{6^2-4*6k&lt;0}}}

{{{36-24k&lt;0}}}

{{{36&lt;24k}}}

{{{k&gt;36/24}}}

{{{k&gt;6/4}}}

{{{k&gt;3/2}}}

{{{k&gt;1.5}}}

if {{{k=2}}}-&gt;

{{{ graph( 600, 600, -10, 10, -10, 10, 6x^2 + 6x + 2) }}}

</PRE>