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Quadratic equations

A quadratic equation can be written as $ax^2 + bx + c = 0$ with $a e 0$ . It can be solved with the quadratic formula. The expression under the root, the discriminant $b^2 - 4ac$ , tells how many solutions there are: two if it is positive, one if it is zero and no real ones if it is negative.

Try it yourself

The quadratic function

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

the quadratic formula

D = b^2 - 4ac

the discriminant

Symbols

$a,\ b,\ c$	coefficients
$D$	discriminant

Example

$x^2 - 5x + 6 = 0$ :

$x = \frac{5 \pm \sqrt{25 - 24}}{2}$ , so $x = 3$ or $x = 2$ .

Substitute the solutions back into the equation and check that the left side becomes zero.

Practise algebra and equations for free →

Systems of two equations →

Part of Mathematics 1T: Algebra and equations.