C. 857. Find the pairs (c,d) for which the equation x³-8x²+cx+d=0 has three (not necessarily) different positive integer roots.

(5 points)

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Sorry, the solution is published in Hungarian only.

Megoldás: Az gyöktényezős alakból kapjuk, hogy x₁+x₂+x₃=8.

Az egyenlet megoldás számhármasai: (1,1,6); (1,2,5); (1,3,4); (2,2,4); (2,3,3).

Vagyis a megoldások: (13,-6); (17,-10); (19,-12); (20,-16); (21,-18).

Statistics on problem C. 857. 117 students sent a solution. 5 points: 96 students. 4 points: 10 students. 3 points: 2 students. 0 point: 8 students. Unfair, not evaluated: 1 solution.