Fundamental Mathematics/Arithmetic/Polynomial Equation

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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