Expii

Solving Quadratic Inequalities with No Roots - Expii

If you have a quadratic function f(x) with no real roots, then the graph y = f(x) is either an upward parabola with vertex above the y-axis, or a downward parabola with vertex below the y-axis. So either f(x) > 0 for all x, or f(x) < 0 for all x. Either way, you can easily describe the solutions of f(x) > 0, f(x) ≥ 0, f(x) < 0, or f(x) ≤ 0, whichever you want to solve.