Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
Already signed up?
New to KöMaL?

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).


Statistics:

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 solutions.

Problems in Mathematics of KöMaL, May 2006