All courses › Foundations of Mathematics › Quadratic equation

Quadratic equation

A quadratic equation $ax^2+bx+c=0$ is solved with the quadratic formula. The expression under the root sign, the discriminant $D$ , tells us how many solutions we get.

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

the quadratic formula

D = b^2 - 4ac

the discriminant

Symbols

$a,\ b,\ c$	coefficients in $ax^2+bx+c=0$
$D$	discriminant

Example

$x^2 - 2x - 8 = 0$ : $D = 4+32 = 36$ , so $x = \frac{2\pm 6}{2} = 4$ or $-2$ .

D>0

gives two solutions,

D=0

gives one, and

D<0

gives no real solutions.

Practise algebra and equations for free →

← Linear equation · Linear function →

Part of Foundations of Mathematics: Algebra and equations.