SOLUTION: What is the average of the roots of {{{x^3+x^2-x-1}}}?

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Question 1150333: What is the average of the roots of x%5E3%2Bx%5E2-x-1?
Found 2 solutions by nijneweed, ikleyn:
Answer by nijneweed(6) About Me  (Show Source):
Answer by ikleyn(52777) About Me  (Show Source):
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Since the given polynomial is of the degree 3, it has 3 roots, according to Algebra Main theorem.


The sum of these roots is equal to the coefficient at x^2, taken with the opposite sign, according to Vieta's theorem.


Thus the sum of the three roots is equal to  -1.


Then the average of the three roots is  -1%2F3.  ANSWER