Question

If a quadratic equation is greater than equal to zero
Then why must D of that equation less than equal to zero
(If D is negative then roots will not be real ? )

Answer 1

For D > 0, the ax^2 + bx + c = 0 will have two real roots, so there will be two values of x for which the expression will be zero and between those two real values the expression will be negative or positive depending a >0 or a < 0. For D <0 and a > 0 there will be no real values of x for which expression will be zero or negative, so its graph will be parabola lying above the x-axis. So the value of expression is always positive.