1964 AHSME Problems/Problem 24
Contents
Problem
Let constants. For what value of is a minimum?
Solution 1
Expanding the quadratic and collecting terms gives . For a quadratic of the form with , is minimized when , which is the average of the roots.
Thus, the quadratic is minimized when , which is answer .
Solution 2
The problem should return real values for and , which eliminates and . We want to distinguish between options , and testing should do that, as answers will turn into , respectively.
PLugging in gives , or . This has a minimum at , or at . This is answer .
See Also
1964 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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