Question 697245
{{{kx^2+kx+5=0 }}}

If the discriminant {{{b^2 - 4ac = 0}}}, then the solution will have equal roots or only one solution


here {{{b = k}}}
{{{a = k}}}
{{{c = 5}}}

so

{{{k^2 - 4*k*5 = 0}}}

{{{k^2 - 20k = 0}}}

{{{k(k - 20) = 0}}}...since {{{k<>0}}} product will be equal to zero if 

{{{k - 20=0}}}

so

{{{k =20}}}


then you have:

{{{20x^2+20x+5=0 }}}


check if the roots are equal:



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


{{{x = (-20 +- sqrt(20^2-4*20*5 ))/(2*20) }}}

{{{x = (-20 +- sqrt(400-400 ))/40 }}}

{{{x = (-20 +- sqrt(0))/40 }}}

{{{x = (-20 +- 0)/40 }}}

{{{x = -20/40 }}}

{{{x = -1/2 }}}.......so, we have only one root


see it on a graph:


{{{ graph( 600, 600, -5, 5, -5, 5, 20x^2+20x+5) }}}