Subcontests
(4)polynomials whose zeros are exactly a_1,a_2,...,a_n
Find all polynomials P(x)=xn+a1xn−1+...+an whose zeros (with their multiplicities) are exactly a1,a2,...,an. if triangle HML is equilateral, then so is triangle ABC
In a triangle ABC, points H,M,L are the feet of the altitude from C, the median from A, and the angle bisector from B, respectively. Show that if triangle HML is equilateral, then so is triangle ABC.