Question 736470
In the quadratic formula for finding roots, 
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}, the
discriminant is {{{  b^2-4*a*c }}}
This determines the types of solutions
{{{ 4x^2 + 12x + 9 =0 }}}
{{{ a = 4 }}}
{{{ b = 12 }}}
{{{ c = 9 }}}
{{{ b^2 - 4*a*c = 12^2 - 4*4*9 }}}
{{{ b^2 - 4*a*c = 144 - 144 }}}
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The discriminant is {{{ 0 }}}, so there is a single solution,
called a double root {{{ x = -b/(2a) }}}
Here's the plot:
{{{ graph( 400, 400, -4, 2, -2, 10, 4x^2 + 12x + 9 ) }}}