First divide all the coefficients of the polynomial by 2019: x*2018 - (2018/2019)x^2017 + (2017/2019)x^2016 - ... + (3/2019)x^2 - (2/2019)x + 1/2019 = 0.
The formula for the harmonic mean is H = 2018 / (1/x_1 + 1/x_2 + ... + 1/x_2018).
Multiply the numerator and denominator by the product of all 2018 terms:
2018 * (x_1*x_2*...*x_2017*x_2018) / (x_2*...*x_2017*x_2018 + x_1*x_3*...*x_2017*x_2018 + x_1*x_2*x_4*...*x_2017*x_2018 + ...... + x_1*x_2*...*x_2016*x_2018 + x_1*x_2*...*x_2016*x_2017)
Now the numerator is 2018 times the constant term of the polynomial and the denominator is the linear coefficient of the polynomial. Then H = 2018 * (1/2019) / (-2/2019) = -1009
Edited on March 15, 2019, 1:31 am
Solution
