Lesson 4
1. Lesson 4
1.7. Explore 3
Module 5: Radicals
Example 3: Solving Radical Equations with the Quadratic Equation
Solving radical equations can also include the need to use the quadratic equation. For example, how would you find the roots of the following equation?
First you need to notice that x2 − 3 > 0. When solutions are found they need to be checked against this requirement.
a = 1, b = −3, c = −3
The roots of the quadratic equation are 
and 
. However since 
is less than 3, it cannot be a root of the original equation. 
is greater than 3 and is the only permissible root of the original equation.
Example 4: Equations with Two Radicals
In Try This 2 you saw examples of equations that included two radicals. Read through a similar type of example on page 298 of the textbook. Think about the following questions as you examine the example:
- Why is it more beneficial to isolate the more complex radical before squaring both sides?
- What would happen if you isolate the simple radical
and then square both sides?