### Fractions and Roots

Fractions of the form

are obtained in LaTeX using the construction
`\frac{`

*numerator*`}{`

*denominator*`}`

.

For example, to obtain

one would type
The function $f$ is given by
\[ f(x) = 2x + \frac{x - 7}{x^2 + 4}\]
for all real numbers $x$.

To obtain square roots one uses the control sequence

`\sqrt{`

*expression*`}`

.

For example, to obtain

one would type
The roots of a quadratic polynomial $a x^2 + bx + c$ with
$a \neq 0$ are given by the formula
\[ \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

In LaTeX, an
*n*th root is produced using

`\sqrt[n]{`

*expression*`}`

.

For example, to obtain

in LaTeX, one would type
The roots of a cubic polynomial of the form $x^3 - 3px - 2q$
are given by the formula
\[ \sqrt[3]{q + \sqrt{ q^2 - p^3 }}
+ \sqrt[3]{q - \sqrt{ q^2 - p^3 }} \]
where the values of the two cube roots must are chosen
so as to ensure that their product is equal to $p$.