Urgent! Els polinomis ax ^ 3-3x ^ 2 + 2x-3 i ax ^ 2-5x + a quan es divideixen per x-2 deixen restes de p i q respectivament. Trobeu el valor de a si p = 3q. Com? Gràcies urgents!

Resposta:

# a = 19/7, p = 75/7, q = 25/7 #

Trucades

# f_1 (x) = ax ^ 3-3x ^ 2 + 2x-3 #

# f_2 (x) = ax ^ 2-5x + a #

Ho sabem

# f_1 (x) = q_1 (x) (x-2) + p # i

# f_2 (x) = q_2 (x) (x-2) + q #

tan

# f_1 (2) = 8a-12 + 4-3 = p #

# f_2 (2) = 4a-10 + a = q # i també

# p = 3q #

Resoldre

# {(8a-11 = p), (5a-10 = q), (p = 3q):} #

obtenim

# a = 19/7, p = 75/7, q = 25/7 #