# Quadratic equations

A **quadratic equation** is any equation that can be put into the following general form:

$ax^2+bx+c=0$

The requirement is that $a \ne 0$. $a$, $b$ and $c$ are **coefficients**.

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### Note

A quadratic equation can have either one, two or no solutions.

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### Remember

The equation $x^2+px+q=0$ is called the

**canonical form**of the quadratic equation. It is possible to put every quadratic equation in the canonical form.To bring a quadratic equation into canonical form, the whole equation is divided by the coefficient $a$ (the number that precedes $x^2$).

$ax^2+bx+c=0$ $|:a$

$x^2+\frac{b}{a}x+\frac{c}{a}=0$

$x^2+\frac{b}{a}x+\frac{c}{a}=0$

### Example

Put the equation $2x^2+8x+7=0$ in the canonical form.

$2x^2+8x+7=0$ $|:2$$x^2+4x+3.5=0$