Nujno! Polinomi ax ^ 3-3x ^ 2 + 2x-3 in ax ^ 2-5x + a, ko jih delimo s x-2, pustimo ostanke p in q. Poišči vrednost a, če je p = 3q. Kako? Nujno hvala!

Odgovor:

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

Pojasnilo:

Klicanje

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

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

to vemo

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

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

tako

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

# f_2 (2) = 4a-10 + a = q # in tudi

# p = 3q #

Reševanje

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

dobimo

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