Question 952836
In order to have 1 rational root, you have
to make {{{ sqrt( b^2-4*a*c ) = 0 }}} in
the quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
-----------------------------------
{{{ 3x^2 - 6x + c = 0 }}}
{{{ a = 3 }}}
{{{ b = -6 }}}
{{{ c = c }}}
{{{ sqrt( b^2 - 4*a*c ) = 0 }}}
{{{ sqrt( (-6)^2 - 4*3*c ) = 0 }}}
{{{ sqrt( 36 - 12c ) = 0 }}}
{{{ 36 - 12c = 0 }}}
{{{ 12c = 36 }}}
{{{ c = 3 }}}
The equation for finding the roots is:
{{{ 3x^2 - 6x + 3 = 0 }}} 
Here's the plot:
{{{ graph( 400, 400, -5, 5, -3, 10, 3x^2 - 6x + 3 ) }}}
As you can see, it touches the x-axis in one place,
meaning 1 rational root