1Cademy - Discriminant of a Quadratic Equation

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Quadratic Formula

Definition

Discriminant of a Quadratic Equation

The discriminant is the expression $b^2 - 4ac$ that appears underneath the square root in the Quadratic Formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . For a quadratic equation written in standard form $ax^2 + bx + c = 0$ , the discriminant is calculated by squaring the coefficient of the linear term and subtracting four times the product of the leading coefficient and the constant term. Because the discriminant sits inside the radical, its value controls whether the expression under the square root is positive, zero, or negative — and therefore determines how many real solutions the Quadratic Formula produces.