Question 1: Solve the quadratic equation .
Answer: The two solutions are given by the quadratic formula
where , , and . Therefore, after some simplification, the two solutions are and .
I don’t like much how there is an ambiguity here. It seems to suggest we’d need more information if we actually wanted to know in a real problem. Sure, if we knew was positive, we’d take the positive solution, and conversely if it’s negative. But how would we ever know that?
To solve this problem, I propose an alternative methodology. Let’s assume is actually the solution. From this we can prove that . And since zero is greater than , we can also say . Yep. I propose this as a general procedure for solving quadratic equations. Using the quadratic formula, take the root with the plus sign, not the minus sign. Then use it to derive an inequality that you know for certain is true. This way, you don’t need to
rely on extra assumptions to determine which root is correct, and there is no ambiguity, unlike in the religion.