# Math 2 example statements

https://arbital.com/p/56p

by Joe Zeng Jul 7 2016 updated Jul 7 2016

If you can read these formulas, you're in Math 2!

If you're at a Math 2 level, you'll probably be familiar with most or all of these sentences and formulas, or you would be able to understand what they meant on a surface level if you were to look them up.

The [-quadratic_formula] states that the roots of every quadratic expression $ax^2 + bx + c$ are equal to $\displaystyle \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. The expression under the Square root, $b^2 - 4ac$, is called the [-discriminant], and determines how many roots there are in the equation.

The imaginary number $i$ is defined as the primary root of the quadratic equation $x^2 + 1 = 0$.

To solve the system of linear equations $\begin{matrix}ax + by = c \\ dx + ey = f\end{matrix}$ for $x$ and $y$, the value of $x$ can be computed as $\displaystyle \frac{bf - ce}{bd - ae}$.

The [-power_rule] in calculus states that $\frac{d}{dx} x^n = nx^{n-1}$.

All the solutions to the equation $m^n = n^m$ where $m < n$ are of the form $m = (1 + \frac 1x)^x$ and $n = (1 + \frac 1x)^{x+1}$, where $x$ is any positive real number.