#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.
