1971 AHSME Problems/Problem 22
Problem
If is one of the imaginary roots of the equation , then the product is equal to
Solution 1
Expanding the given expression yields . Recalling that , we see that this expression equals . By the properties of roots of unity , , so the given expression equals .
Solution 2 (not recommended)
Suppose . Substituting this into the given expression, we can calculate the result:
See Also
1971 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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