Identifying Extraneous Roots:
Extraneous roots are found when a variable discovered after solving an equation is not true if used in the original equation. In other words, it’s a root found by squaring both sides, it is not a root in the equation you started with. To show this, we could use an equation like .
First we will square both sides
This will remove the radical sign
x – 1 = 2x + 2
Then we take away x from the left side and from the right side. We take away 2 and put it on the left side.
-3 = x
If we plug x back in as -3 it will not work.
A radicand of a square root cannot be negative.
Another example of this would be:
We will take away five from both sides
Then we square both sides
3x – 1 = 9
We will now add one to both sides
3x = 10
Divide both sides by 3
If we plug this in to the original equation (After taking away 5 from both sides) this happens,
3 does not equal -3
Therefore, this root is not accurate when used with the original equation. This makes it a root that is not real, or extraneous.