This site is supported by donations to The OEIS Foundation.
Quadratic polynomials
From OeisWiki
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)