Question

part b
check for extraneous roots.
select the word(s) from the drop - down list to correctly complete the sentence.
show hints
the solution an extraneous root.

Explanation:

To determine if the solution has an extraneous root, we need to know the original equation (which is not provided here). However, typically, when checking for extraneous roots, we substitute the solution back into the original equation (especially if it involved operations like squaring both sides, taking reciprocals, etc. that can introduce extraneous roots). If the substituted value does not satisfy the original equation, then it is an extraneous root. Since the problem is about checking for extraneous roots (a concept in Algebra, a subfield of Mathematics), and assuming a common scenario (e.g., from an equation where extraneous roots can occur), a common case is that "The solution has an extraneous root" or "The solution does not have an extraneous root" depending on the equation. But since the original equation is missing, we can't be certain. However, if we assume a typical problem (like solving a radical equation where squaring leads to an extraneous root), the drop - down likely has options like "has" or "does not have". For example, if after substitution the solution doesn't satisfy the original equation, the answer is "has". If it does, the answer is "does not have".

To check for an extraneous root, substitute the solution into the original equation. If it fails to satisfy the equation, it's extraneous. Without the original equation, but based on common problems (e.g., radical equations), the likely answer depends on substitution. If the solution doesn't satisfy the original equation, the answer is "has".

Answer:

The solution \boxed{has} an extraneous root. (Note: This answer is based on common problem scenarios. If the original equation's solution satisfies it, the answer would be "does not have".)