Quadratic Equations

Gives the roots of the standard quadratic equation ax^2 + bx + c = 0 with a \neq 0.

Determines the existence and nature of the roots of a quadratic equation with real coefficients.

Gives the magnitude of the difference between the roots of ax^2 + bx + c = 0.

States that non-real complex roots of a real quadratic polynomial always occur in conjugate pairs.

Relates the sums of powers of roots of ax^2 + bx + c = 0 for integers n \ge 2.

Gives the turning point coordinates and the minimum or maximum value of y = ax^2 + bx + c.

Gives the necessary and sufficient condition for a quadratic expression to be strictly positive everywhere.

Condition for a real number k to lie strictly between the real roots \alpha and \beta.

Gives conditions for two quadratic equations to have both roots or exactly one root in common.