Math 2 example statements

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.