Quadratic discriminants and roots of a quadratic
This file defines the discriminant of a quadratic and gives the solution to a quadratic equation.
Main definition
The discriminant of a quadratic a*x*x + b*x + c is b*b - 4*a*c.
Main statements
• Roots of a quadratic can be written as (-b + s) / (2 * a) or (-b - s) / (2 * a),
where s is the square root of the discriminant.
• If the discriminant has no square root, then the corresponding quadratic has no root.
• If a quadratic is always non-negative, then its discriminant is non-positive.
Tags
polynomial, quadratic, discriminant, root
If a polynomial of degree 2 is always positive, then its discriminant is negative, at least when the coefficient of the quadratic term is nonzero.