SOLUTION: The roots of (x^3) + 2p(x^2) - px + 10 = 0 are integral and form an arithmetic sequence. What is the value of p?
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Question 1191255: The roots of (x^3) + 2p(x^2) - px + 10 = 0 are integral and form an arithmetic sequence. What is the value of p? Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52790) (Show Source):
The three roots are integers in arithmetic progression, and their product is -10. Quick trial and error shows the roots are -1, 2, and 5. The polynomial is
Equate the coefficients of that polynomial and the polynomial in its given form to see that p = -3.
