## anonymous 4 years ago Using complete sentences, explain what the discriminant is and what it tells you about the solutions of a quadratic equation. Provide a unique example to back up your explanation, please help

Let the discriminant by denoted by D. $D:=b2−4ac$ Which corresponds to the general quadratic equation: $ax2+bx+c=0$ where a,b and c are real numbers. Recall that the solutions of this general quadratic equation are given by $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ If $b2−4ac<0$ then the quadratic has no real solutions (actually, has two complex conjugate pairs. If $b2−4ac=0$ then the quadratic has one distinct (i.e. one and only one) real solution, i.e.$x \in \mathbb{R}$ If $b^2-4ac >0$ then the quadratic has two distinct real solutions.