z.1 a) x^2 - x - 6 = 0 delta = (-1)^2 - 4*1*(-6) = 1 + 24 = 25 p(delty) = 5 x1 = [ 1 - 5]/2 = -4/2 = -2 x2 = [ 1 + 5]/2 = 6/2 = 3 ========================== b) 4x - 4 x^2 = 1 4 x^2 - 4x + 1 = 0 (2x - 1)^2 = 0 2x - 1 = 0 2x = 1 x = 1/2 - pierwiastek podwójny ============================= z.2 a) x^3 - 2 x^2 + 4x - 8 = 0 x^2 *(x - 2) + 4*(x - 2) = 0 ( x^2 + 4)*( x - 2) = 0 x - 2 = 0 , bo x^2 + 4 > 0 dla dowolnej liczby rzeczywistej x x = 2 ===== b) x^3 + 9 x^2 - x - 9 = 0 x^2 *( x + 9) - 1*(x + 9) = 0 (x^2 - 1)*(x + 9) = 0 (x -1)*(x + 1)*( x + 9 ) = 0 x - 1 = 0 lub x + 1 = 0 lub x + 9 = 0 x = 1 lub x = -1 lub x = - 9 ==============================
