2230.62 – Two Quadratics
Suppose the quadratic equation has roots and AND the quadratic equation has roots and . Then what is the value of ?
Therefore, and . Similarly, and . Therefore,
Using similar reasoning, , therefore,
Now if then cancels in the preceding equation and we learn that Parallel reasoning says that and from this follows that . So the answer to the problem is , and the given equations are the single equation .
However, if then it is easy to show that so both given equations are and the answer is .