Question 733309
The discriminant is {{{ b^2 - 4a*c }}} in the
quadratic formula {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{ x^2 + 6x + 9 = 0 }}}
{{{ a = 1 }}}
{{{ b = 6 }}}
{{{ c = 9 }}}
{{{ b^2 - 4a*c = 6^2 - 4*1*9 }}}
{{{ b^2 - 4a*c = 36 - 36 }}}
{{{ 36 - 36 = 0 }}}
When the discriminant is {{{ 0 }}}, there is
a single real solution ( called a double root )
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{{{ x^2 + 2x - 8 = 0 }}}
{{{ a = 1 }}}
{{{ b = 2 }}}
{{{ c = -8 }}}
{{{ b^2 - 4a*c = 4 - 4*1*(-8) }}}
{{{ b^2 - 4a*c = 4 + 32 }}}
{{{ b^2 - 4a*c = 36 }}}
The discriminant is positive, so there
are 2 real solutions
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Here are plots of both equations:
{{{ graph( 400, 400, -10, 10, -10, 10, x^2 + 6x+ 9, x^2 + 2x - 8 ) }}}