1962 AHSME Problems/Problem 11
Problem
The difference between the larger root and the smaller root of is:
Solution
Call the two roots and , with . By Vieta's formulas, and (Multiplying both sides of the second equation by 4 gives .) The value we need to find, then, is . Since , . Subtracting from both sides gives . Taking square roots, . (Another solution is to use the quadratic formula and see that the roots are , and their difference is 1.)
See Also
1962 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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