nglasser@yale-com.UUCP (Nathan Glasser) (10/22/83)
The following is a solution to the problem I posted earlier. The problem
was to find the sum of the seventeenth powers of the roots of the equation
17 2
x + 3x + 2x - 1 = 0.
Let the roots of this equation be X , i = 1,2,...,17.
i
Also let S denote the sum of the kth powers of the roots of the given equation.
k
Then since each X is a root of the equation,
i
17 2
X + 3X + 2X - 1 = 0 for each i. If we add all 17 such equations
i i i we get
S + 3S + 2S - 17 = 0.
17 2 1
>From the coefficients of the polynomial, it is clear that S = 0. Also,
2 1
S , the sum of the squares of the roots = S - 2(X X + ... + X X ).
2 1 1 2 16 17
But the sum of the products of the roots taken two at a time = the coeff.
of the x^15 term, which is 0. So S = 0. Hence S = 17.
2 17
Flames to
Nathan Glasser
..decvax!yale-comix!nglasser