# Fundamental Mathematics/Arithmetic/Polynomial Equation

## Polynomial Equation[edit | edit source]

Polynomial Equation has general form

## 1st ordered polynomial equation[edit | edit source]

1st ordered polynomial equation general form

Divide the quadratic equation by *a*, which is allowed because *a* is non-zero:

In summary,

- 1st ordered polynomial equation has root

## 2nd ordered polynomial equation[edit | edit source]

2nd ordered polynomial equation has general form

The quadratic formula can be derived with a simple application of technique of completing the square.Divide the quadratic equation by *a*, which is allowed because *a* is non-zero:

Subtract *c*/*a* from both sides of the equation, yielding:

The quadratic equation is now in a form to which the method of completing the square can be applied. Thus, add a constant to both sides of the equation such that the left hand side becomes a complete square:

which produces:

Accordingly, after rearranging the terms on the right hand side to have a common denominator, we obtain:

The square has thus been completed. Taking the square root of both sides yields the following equation:

Isolating *x* gives the quadratic formula:

## Summary[edit | edit source]

**Polynomial Equation****Equation****Root**1st ordered equation 2nd ordered equation