Find the values of k for which the equation 3y^2-2y+k=0 has one rational root. (Hint. What should the discriminant be for there to be one rational root?)

Question

amriju · Answer

discriminant should be a rational number for the overall solution to be rational..so discriminant should be a perfect square...so b^2-4ac thats 4-12k should be a perfect square....now we are asked to find one rational root...so the roots must be same...so the discriminant must be 0...which is a perfect square...hence we have k=1/3

amriju · Answer

if there would be two rational solns...thn...k could be 0 or 1/4