GMAT Exam: A Simple Guide To Algebra - Quadratic Equations

A quadratic equation is an equation that can be expressed in standard form as ax2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0.

The roots are the values for the variable that make the quadratic equation true.

When you are restricted to real numbers (as is the case for the GMAT), a quadratic equation has two distinct real roots, one real root, or no real roots in its solution set.

Solving Quadratic Equations of the Form x2 = k, (k ≥ 0)
The equation x2 = k, (k ≥ 0), has solution or .

Commonly, you write this solution as .

Here are examples.


Solving Quadratic Equations by Factoring
When you solve quadratic equations by factoring, you use the following zero factor property: If the product of two numbers is 0, then at least one of the numbers is 0.

To solve a quadratic equation by factoring: Put the equation in standard form, factor the nonzero side of the equation, set each factor equal to zero, and then solve the resulting linear equations for the variable.

Here is an example.

Solve x2 + x = 6.

Solve x2 + 5x = 0.