Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Advanced Algebra And Systems Of Equations
Introduction: The Zero Product Property
Solving quadratic equations by factoring relies on a fundamental mathematical principle: if the product of two factors equals zero, then at least one of the factors must be zero. This is called the zero product property.
This lesson demonstrates how to use factoring to find the roots of quadratic equations, where the quadratic expression is set equal to zero.
The Zero Product Property
The zero product property states:
If a × b = 0, then a = 0 or b = 0 (or both).
This property allows us to solve equations after factoring, because we can set each factor equal to zero and solve separately.
The General Process
| Step | Action | | 1 | Set the quadratic equation equal to zero | | 2 | Factor the quadratic expression | | 3 | Set each factor equal to zero | | 4 | Solve each resulting linear equation | | 5 | List both solutions |