## Latex Example

\documentclass[a4paper,11pt]{article}

\begin{document}
The quadratic equation $f(x)=x^2+px+q$ has zero, one or two roots.
To see this we add a term to create a complete square:

$$x^2+px+q=0$$

$$x^2+px+\frac{1}{4}p^2 = \frac{1}{4}p^2 -q$$

Now we can apply the binomial equation:

$$\left( x+\frac{p}{2} \right)^2 = \frac{1}{4}p^2 -q$$

We take the square root on both sides of the equation

$$x+\frac{p}{2} = \sqrt{\frac{p^2}{4} -q}$$

to get

$$x_{1,2} = -\frac{p}{2} \pm \sqrt{\frac{p^2}{4} -q}$$

The expression in the root

$$D = {\frac{p^2}{4} -q}$$

is called discriminant''. The quadratic equation has two real roots
for $D>0$ and none for $D<0$. If $D=0$,
we have a double root.
\end{document}


Peter Junglas 8.3.2000