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Sign chart

A quadratic inequality is solved by finding the zeros and studying the sign between them. The zeros split the number line into intervals. In each interval the expression has the same sign, so it is enough to test one number there. The parabola opens upwards when the coefficient of x squared is positive, and then the expression is positive outside the zeros. Remember whether the zeros themselves should be included.

Symbols

Example

$x^2 - 4x + 3 = 0$ has roots $x = \dfrac{4 \pm \sqrt{16 - 12}}{2}$, that is $x = 1$ and $x = 3$.

$x^2 - 4x + 3 > 0$ when $x < 1$ or $x > 3$.

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Part of Mathematics S1: Inequalities and sign charts.