{"conversations": [{"from": "user", "value": "Pots donar-me un formulari generalitzat per trobar totes les arrels d'un polinomi al grau no-th utilitzant el m\u00e8tode del nouton?"}, {"from": "assistant", "value": "La forma generalitzada del m\u00e8tode Newton per a trobar les arrels d' un polinomi a l' angle n \u00e9s donada per l' equaci\u00f3 seg\u00fcent: Xk+1 = Xk - (f(Xk)/f' XXk) on Xk \u00e9s una suposici\u00f3 inicial i F(Xk) \u00e9s el valor del polinomi avaluat a Xk, i '( fXk) \u00e9s la derivada del polinomi a Xk."}, {"from": "user", "value": "Em pots donar exemples?"}, {"from": "assistant", "value": "# ## Exemple 1: Cerca una arrel de la funci\u00f3 q quadr\u00e0tica f(x) = x^2 - 4 Defineix la funci\u00f3 derivada: f(x) = x^2 - 4 f'(x) = 2x Trieu una suposici\u00f3 inicial, diguem X0 = 1. Aplica la f\u00f3rmula de Newton- molson: X1 = X0 (f(X0) / X ((X0) = 1 - 1 (1^2) 4) / 4 * 1) = 1, 5 = 1. 5 = 1. 5 = 1. 5 = 1 = 2. 5 = 1 = 1 = 1, 5 x = 1 = 1, x = X2x - X1 (( fX) = 2. 5 (5) / 12. 5) / 5; 5) El m\u00e8tode d' RALL = 1 = 1 = 1 = 1, 2 x = 1 = 4x (x) / x = 1 = 1 = 4x) / x = 1, que \u00e9s l' igual que \u00e9s l' 1. 5 x = 1 = 1, 2 x = 1 = 1, 2 x = 1, 2 x = 4x) / x = 1, 2 x = 1, 2 x = 1, 2 x = 4x) / x = 4x (x) / X (x) / x = 1, 2 x = 4x) / X = 1 = 1 = 1 = 1 = 1 = 1 = 1, que \u00e9s l' igual que \u00e9s l' 1. 5x) / X (x) / X^2) / X (x) / X = 1 = 1 = 1 = 4x) / X (x) / X (x) / x = 1 = 1, 5) = 1, que \u00e9s l' igual que \u00e9s l' igual que \u00e9s l' igual que \u00e9s l' igual que \u00e9s l' igual que \u00e9s l' 1. 5x) / x = 1, 2 x = 1, i = 1, 2 x = 1, 2 x = 1, 2 x = 1, x = 1 = 1, 2 x = 1, x = 1, 5) = 1, 2 = 1, 2 x = 1, 2 x = 1, 2 = 1, 2x) / x = 1 = 1 = 1, x = 1, 2 x = 1, 2 x = 1, 2 = 1 = 1, 2 = 1, 2 x = 1, 2 x = 1, 2 x = 4x) / x = 1, i"}]}