1.5 – Equations
Video 1 of 3: Quadratic Equations and Completing the Square
Video 2 of 3: Quadratic Formula
Video 3 of 3: Rational and Radical Equations
Properties of Equalities
A Linear Equation of one variable is an equation equivalent to one of the form
where and are real numbers and is a variable.
A Quadratic Equation is an equation equivalent to one of the form
where and are real numbers, and
Solutions of a Simple Quadratic Equation
The solutions of the equation are , and
Completing the Square
To make the equation a perfect square, is added (typically to both sides of an equation)
The Quadratic Formula
The roots of a quadratic equation of the form , with are
The Discriminant of the general quadratic equation where is
1. If , then the equation has two distinct real solutions.
2. If , then the equation has exactly one real solution.
3. If , then the equation has no real solution.