Discriminants (Leaving Cert Mathematics): Flashcards

$D = b^2 - 4ac$

Two distinct real roots

One real root (or two equal real roots)

No real roots (complex conjugate pairs)

$ax^2 + bx + c = 0$ where $a \neq 0$

Under the square root: $\sqrt{b^2 - 4ac}$

$D > 0$

$D = 0$

Complex (conjugate pairs)

Nature of roots of quadratic equation