<prompt> Zingatia polynomia Px x6-x5-x3-x2-x na Qxx4-x3-x2-1. Ikizingatiwa kuwa z_1, z_2, z_3, na z_4 ndio mizizi ya Qx0, pata Pz_1Pz_2Pz_3Pz_4.  <response>: Tunafanya mgawanyiko wa polynomial na Px kama mgao na Qx kama kigawanyo, tukitoa beginaligned Px x6-x5-x3- x2-x x21 x4-x3-x21 x2-x1 x21 Qx x2-x1. endalignedKwa hivyo, ikiwa z ni mzizi wa Qx 0, basi usemi wa Pz ni rahisi sana, kwa sababu beginaligned P z ghairiz21Qz z2-z1 z2-z1. mwishoiliyopangwaInafuata kwamba sum_i14 Pz_i sum_i14 z_i2 - z_i 1.Kwa fomula za Vieta , sum_i14 z_i 1, na sum_i14 z_i2 kushotosum_i14 z_ikulia2 - 2 sum_1 le i j le 4 z_i z_j 12 - 2 -1 3.Kwa hiyo, sum_i14 Pz_i 3 - 1 4 6. 