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# Discriminant of a quadratic equation

The discriminant $\Tviolet{\Delta}$ of a quadratic equation $$a\Tred{x}^2 + b\Tred{x}+c = 0$$ is the number $$\Tviolet{\Delta} = b^2 - 4 ac.$$ The computation of the discriminant is essential for solving a quadratic equation.

The discriminant of the equation $\Tred{x}^2 - 3\Tred{x} + 2 = 0$ is $$\Tviolet{\Delta} = 3^2 - 4\times 1\times 2 = 9-8 = 1.$$

The discriminant can be positive, negative or zero. The sign of the discriminant tells us whether an equation can be solved.

Equation Discriminant Sign Number of solutions
$x^2 - 3x + 1 = 0$ $9 - 4 = 5$ $\gt 0$ $2$
$x^2 - 2x + 1 = 0$ $4 - 4 = 0$ $= 0$ $1$
$x^2 - x + 1 = 0$ $1 - 4 = -3$ $\lt 0$ $0$