Mathematical and Physical Journal
for High Schools
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Problem C. 857. (May 2006)

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 pont)

Deadline expired on June 15, 2006.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás: Az \left(x-x_1\right)\left(x-x_2\right)\left(x-x_3\right)=0 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).


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.

Problems in Mathematics of KöMaL, May 2006