# Formulae to Solve of Polynomial Equations

## The Linear Formula

The linear formula gives the solution of `a``x` + `b` = 0 for real numbers `a`, `b` with `a` ≠ 0.

## The Quadratic Formula

The quadratic formula gives the solutions of `a``x`^{2} + `b``x` + `c` = 0 for real numbers `a`, `b`, `c` with `a` ≠ 0.

## The Cubic Formula

The cubic formula gives the solutions of `a``x`^{3} + `b``x`^{2} + `c``x` + `d` = 0 for real numbers `a`, `b`, `c`, `d` with `a` ≠ 0.

*Directions: Take *`n` = 0, 1, 2. Use real cube roots if possible, and principal roots otherwise.

## The Quartic Formula

The quartic formula gives the solutions of `a``x`^{4} + `b``x`^{3} + `c``x`^{2} + `d``x` + `e` = 0 for real numbers `a`, `b`, `c`, `d`, `e` with `a` ≠ 0.

*Directions: Choose all possibilities for the three ± signs with the last two equivalent. Use real cube roots if possible, and principal roots otherwise.*