Using the Quadratic Formula (Leaving Cert Mathematics): Flashcards

$ax^2 + bx + c = 0$

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

$b^2 - 4ac$

Two different real solutions

One repeated real solution

No real solutions (complex solutions)

Plus or minus; gives two possible solutions

Coefficient of $x^2$

Coefficient of $x$

Constant term

$a \neq 0$

When factorisation not easy or need exact decimal answers

Identify coefficients $a$, $b$, $c$ in standard form

Works for any quadratic equation