0
This can be easily answered using the well-known formulae for solving quadratic equations:
y = 3x2 - 5x + 1
then
x = (5 +- sqrt(25 - 4*3*1))/6
since 25-4*3*1 = 25-12 = 13, which is > 0, this parabola has two intersections with the x-axis (as the quadratic equation has two real roots).
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