1975 AHSME Problems/Problem 5
The polynomial is expanded in decreasing powers of . The second and third terms have equal values when evaluated at and , where and are positive numbers whose sum is one. What is the value of ?
Solution by e_power_pi_times_i
The second and third term of is and , respectively. For them to be equal when , . For them to be equal when , . Then , so , which simplifies to . Since , .