If a Quadratic $ax^2+bx+c\geq 0,$ then why can't we say Discriminant $D(b^2-4ac)=0$ only and $a>0$?

Question

If a Quadratic $ax^2+bx+c\geq 0,$ then why can't we say Discriminant $D(b^2-4ac)=0$ only and $a>0$?

My Doubt:

When Discriminant $(D=b^2-4ac)=0$ then we obtain quadratic $ax^2+bx+c=0$ as $a(x+\frac{b}{2a})^2$.

Since $a(x+\frac{b}{2a})^2\geq0\; \forall x\in \mathbb R$ if $a>0$.

But when we solve quadratic equation $ax^2+bx+c\geq0$ we do $D\leq 0.$ Why can't we do only $D=0$

Reference Show that if $a > 0$, then $ax^2 + bx + c ≥ 0$ for all values of $x$ if and only if $b^2 − 4ac ≤ 0$.