Library/Algebra/Polynomials/Quadratic trinomial/Quadratic equations and systems of equations

Quadratic equations and systems of equations

Overview
Important

A quadratic equation in one variable has the general form ax2+bx+c=0ax^2 + bx + c = 0, with a≠0a \neq 0. Solutions to quadratic equations are called roots. A system of equations may include a quadratic and a linear equation, or two quadratics, and solving the system means finding all values that satisfy all equations at once.

Important properties

  • Quadratic equations can have 0, 1, or 2 real solutions, depending on the discriminant b2−4acb^2 - 4ac.

  • The quadratic formula x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} gives the solutions.

  • Systems involving a quadratic and a linear equation can be solved by substitution or elimination.

  • Graphically, the solutions to a system correspond to intersection points of the curves.