How do you find out if a solution is an extraneous solution?
To find whether your solutions are extraneous or not, you need to plug each of them back in to your given equation and see if they work. It’s a very annoying process sometimes, but if employed properly can save you much grief on tests or quizzes.
What does it mean to check for extraneous solutions?
Extraneous solutions are values that we get when solving equations that aren’t really solutions to the equation.
How do you check for extraneous roots?
Example: you work on an equation and come up with two roots (where it equals zero): “a” and “b”. When you put “a” into the original equation it becomes zero, but when you put in “b” it doesn’t. So “b” is an extraneous root. This often happens when we square both sides during our solution.
How do you check for extraneous solutions in a rational equation?
If a solution is a restriction, then it is not part of the domain and is extraneous. When multiplying both sides of an equation by an expression, distribute carefully and multiply each term by that expression. If all of the resulting solutions are extraneous, then the original equation has no solutions.
How do you check for extraneous solutions in absolute value equations?
To check if any of your roots are extraneous, plug each of the roots back in to the original equation. If the root does not solve the original problem, then it is extraneous and is not a one of the solutions.
When should you check for extraneous solutions?
You only need to worry about the extraneous root in the case of a quadratic equation if you made the equation quadratic by multiplying by a variable. Any time you square a negative number or a variable (which may be negative), you risk losing information by making it positive.
Why is it important to check for extraneous solutions?
Incorrect values of the variable, such as those that are introduced as a result of the squaring process are called extraneous solutions. Extraneous solutions may look like the real solution, but you can identify them because they will not create a true statement when substituted back into the original equation.
How do you know if an absolute value is extraneous?