When a question asks you to "find all real a and b", it is asking you to find all possible values for the variables a and b that satisfy the given equation or set of conditions. These values must be real numbers, meaning they can be positive, negative, or zero and do not include any complex numbers.
Finding all real a and b is important because it allows us to fully understand and solve a mathematical problem or equation. By finding all possible values for the variables, we can determine the range of solutions and make more accurate predictions or conclusions.
The process of finding all real a and b depends on the specific equation or problem given. Generally, it involves using algebraic manipulations, substitution, or graphing to determine the values that satisfy the given conditions. It may also require using mathematical rules and properties to simplify the problem and eliminate any extraneous solutions.
Yes, it is possible for there to be more than one set of real solutions for a and b. This is especially common when dealing with equations or problems involving multiple variables or conditions. It is important to carefully consider all possible solutions and check for any restrictions or limitations on the values of a and b.
Some common mistakes to avoid when finding all real a and b include forgetting to check for extraneous solutions, not simplifying the problem or equation properly, and not considering all possible values for the variables. It is important to double-check your work and ensure that your solutions make sense in the context of the problem.