4/3x^2-2x+3/4 = 0 is of the form ax^2+bx+c = 0 with a=4/3, b = -2 and c=3/4.
The discriminant is given by the formula:
Delta = b^2-4ac = (-2)^2 - (4xx(4/3)xx(3/4))
= 4 - 4 = 0
Since Delta = 0, the quadratic has one repeated rational root.
The possible cases are:
Delta < 0 The quadratic has no real roots. It has two complex roots that are conjugates of one another.
Delta = 0 The quadratic has one repeated root. If the coefficients of the quadratic are rational then that repeated root is rational too.
Delta > 0 The quadratic has two distinct real roots. If Delta is a perfect square and the coefficients of the quadratic are rational then those roots are rational too.
