The Discriminant and Nature of Quadratic Roots

Vocabulary flashcards covering the definition of the discriminant, its calculation, and how its value determines the number and type of roots for quadratic equations.

Discriminant

The expression $b^2 - 4ac$ for a quadratic equation in the form $ax^2 + bx + c = 0$, which determines the type and number of roots.

Roots when $D > 0$ and is a perfect square

$2$ real, rational roots.

Roots when $D > 0$ and is NOT a perfect square

$2$ real, irrational roots (containing a radical).

Roots when $D = 0$

$1$ real, rational root (also referred to as a double root).

Roots when $D < 0$ (Negative)

$2$ complex roots (complex conjugates, or $2$ nonreal roots).

Double root

The single real, rational root produced when the discriminant of a quadratic equation equals zero ($D = 0$).

Discriminant calculation for $5x^2 - 3x + 2 = 0$

$b^2 - 4ac = (-3)^2 - 4(5)(2) = 9 - 40 = -31$ (using $a = 5$, $b = -3$, $c = 2$).