1975 AHSME Problems/Problem 27
If and are distinct roots of , then equals
If is a root of , then , or Similarly, , and , so
By Vieta's formulas, , , and . Squaring the equation , we get Subtracting , we get
Therefore, . The answer is (E).
We know that . By Vieta's formulas, ,, and . So if we can find , we are done. Notice that , so , which means that