If you have a quadratic function f(x) with 2 or 1 real roots, then it factors as f(x) = a(x-r)(x-s), where a is the leading coefficient (positive or negative), and r and s are the real roots (possibly with r=s). From the factored form, you can then solve the inequality f(x) ≥ 0 by thinking about where f is positive and where it's negative. Solving f(x) > 0, f(x) ≤ 0, or f(x) < 0 are all similar.