Quadratic equation

The quadratic equation is a formula for finding the roots of a second-degree polynomial. Any second-degree polynomial in the variable $x$ will be of the form

$ax^{2}+bx+c$

where $a$, $b$, and $c$ are constants and $a$ is not zero (if it was, the polynomial would only be first-degree). The roots of the polynomial are the particular values of $x$ for which the polynomial equals zero. The fundamental theorem of algebra tells us that we should expect there to be two roots for a second-degree polynomial, although they might be equal in some cases. If we call the roots $x_{+}$ and $x_{-}$ then what we are saying is that

$ax_{\pm }^{2}+bx_{\pm }+c=0\ .$

This is where the quadratic equation comes in. It tells us that the solutions $x_{+}$ and $x_{-}$ can always be found from the equation

$x_{\pm }={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}\ .$