# Quadratic formula

## Statement

Consider a quadratic equation of the form:

This is treated as an equation in . The **quadratic formula** is a formula to determine the solutions of this equation. The short version of the formula is that the roots are:

if the expression makes sens; otherwise there are no roots.

To understand the formula, first define the discriminant of the quadratic function as the value . Now, we make three cases:

Case for discriminant | Conclusion for roots | Conclusion for factorization of polynomial |
---|---|---|

positive, i.e., | there are two real roots, given as and | If we denote the roots by , then |

zero, i.e., | there is a single real root with multiplicity two, and that root is | |

negative, i.e., | there are no real roots | the polynomial does not factor, i.e., it is irreducible |