Final answer:
The solution to 2ˣ = 1 is x=0. The equation p(x) + b/p(x) = c could potentially be a quadratic equation if p(x) is a linear term, which can be solved using the quadratic formula.
Step-by-step explanation:
The question asks about two distinct mathematical equations. The first part of the question, 2ˣ = 1, requires solving for x. This equation is a form of an exponential equation where the base is 2. For any base a (where a > 0 and a ≠ 1), if aˣ = 1, then x must be 0 since any non-zero number raised to the power of 0 equals 1.
The second part of the question, p(x) + b/p(x) = c, doesn't provide a specific type of equation; however, it appears to represent a generic algebraic equation that could be related to rational, polynomial, or possibly quadratic equations, depending on the form p(x) takes.
If p(x) is a polynomial, the equation might become a quadratic equation if we assume p(x) to be a linear term of x. Quadratic equations typically have the form ax² + bx + c = 0 and can be solved using the quadratic formula, which calculates the roots or solutions of the quadratic equation.
Overall, the student is dealing with exponential and quadratic equations which are fundamental concepts in algebra and pre-calculus.