# Explicit expressions for real roots of a quartic equation

## TL;DR

This paper provides explicit, optimized formulas for the real roots of a quartic equation, simplifying the general solution specifically for cases with four real roots.

## Contribution

It introduces a shorter, more efficient set of explicit expressions for real roots of quartic equations, improving upon the general formulas.

## Key findings

- Derived explicit formulas for all four real roots of a quartic.
- Presented a shorter, optimized expression compared to the general quartic solution.
- Enhanced computational efficiency for solving quartics with four real roots.

## Abstract

This short article presents explicit expressions for roots of a quartic equation that has all four real roots. Although a general expression for quartic roots is available on Wikipedia, an optimized and slightly shorter expression for only real roots is presented here.