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  • 5 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

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  1. anonymous
    • 5 years ago
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    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.

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