Final answer:
Without the specific equation, we cannot identify the correct answers regarding the solutions. Generally, quadratic equations have two solutions, but constraints or extraneous results like division by zero can invalidate one of them.
Step-by-step explanation:
To accurately determine the number of solutions to a given equation and whether any of them are extraneous, we need to see the full equation in question. Extraneous solutions can occur when solving equations, especially when dealing with square roots or denominators, as raising both sides of an equation to an even power can introduce solutions that don't actually satisfy the original equation. In quadratic equations or equations with squared variables, two solutions are often found using the quadratic formula. However, depending on the context like physical constraints, sometimes one value is discarded as it does not make sense. If an equation involves denominators, it's important to be alert for values that could result in division by zero, which are not acceptable because they are undefined.
Without the specific equation, we cannot directly choose the accurate statement about the solution(s). But we can derive some general principles from the quadratic formula and other conditions that can make a solution extraneous:
- If the equation is quadratic (or can be reduced to that form), then there will typically be two solutions after applying the quadratic formula.
- Some solutions may be considered extraneous and can thus be discarded if they lead to undefined expressions (such as division by zero) or do not fit the physical constraints of the problem context.
- If a potential solution causes a zero in the denominator of a rational expression, that is an unacceptable or extraneous solution.