Quadratic Equations

An equation of the form ax^2+bx+c=0

An equation of the form ax^2+bx+c=0, where a ≠ 0, is called a quadratic equation. The coefficients a, b, and c may be real or complex numbers.

The values of x that satisfy

The values of x that satisfy the equation are called its roots.

A polynomial equation has at least

A polynomial equation has at least one root. A consequence is that a polynomial equation of degree n has exactly n roots, so a quadratic equation has

The roots of ax^2+bx+c=0 are given

The roots of ax^2+bx+c=0 are given by x = (-b ± sqrt(b^2-4ac))/(2a).

The discriminant is D = b^2

The discriminant is D = b^2-4ac. For real coefficients, it decides the nature of roots.