1989 AHSME Problems/Problem 28
Contents
Problem
Find the sum of the roots of that are between and radians.
Solution
The roots of are positive and distinct, so by considering the graph of , the smallest two roots of the original equation are between and , and the two other roots are .
Then, from the quadratic equation, we discover that the product , which implies that does not exist. The bounds then imply that . Thus which is .
Solution 2
: We treat and as the roots of our equation. Because by Vieta's formula, . Because the principal values of and are acute and our range for is , we have four values of that satisfy the quadratic: Summing these, we obtain . Using the fact that , we get
See also
1989 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 27 |
Followed by Problem 29 | |
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