Question 1089048
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<pre>
The necessary and sufficient condition for it is that the discriminant of the equation must be negative:

d = {{{b^2 -4ac}}} < 0, i.e.

(-6)^2 - 4*a*3 < 0,

36 < 12a,

a > 3.
</pre>

See the plots below for a = 2, 3 and 4.



{{{graph( 330, 330, -5.5, 5.5, -5.5, 5.5,
          2x^2 - 6x +3, 3x^2 - 6x +3, 4x^2 - 6x +3
)}}}


Plot y1 = {{{2x^2 - 6x +3}}} (red), y2 = {{{3x^2 - 6x +3}}} (green), y3 = {{{4x^2 - 6x +3}}} (blue)