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OlympiadSuperchallengeOlympiad Number Theory

Olympiad Number Theory · Superchallenge problem

The roots of z3+z2−22z−40=0z^{3} + z^{2} - 22 z - 40 = 0 are r1,r2,r3r_1, r_2, r_3. Compute ∑ri2\sum r_i^2 and ∑ri3\sum r_i^3.