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# Quadratic polynomials

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(Redirected from Quadratic formula)

A [univariate] **quadratic polynomial** is a [univariate] polynomial of degree 2, i.e. of the form

## Roots of a quadratic equation and the quadratic formula

The two zeros of the quadratic polynomial are the two roots of the quadratic equation

with and .

The two roots are obtained by completing the square, i.e.

or, letting ,

hence

yielding the quadratic formula

where , the discriminant of the quadratic equation, is either:

- 0 (in which case is the rational double root of the quadratic equation);
- positive and a perfect square (the quadratic equation has two distinct rational roots);
- positive and not a perfect square (the quadratic equation has two distinct real conjugate quadratic roots);
- negative (the quadratic equation has two distinct complex conjugate quadratic roots).

## Vieta's formulas for the quadratic

Vieta's formulas for the quadratic

gives a system of two equations in two variables (which are the two roots)