Naliehavé! Polynomy ax ^ 3-3x ^ 2 + 2x-3 a ax ^ 2-5x + a pri delení x-2 zanechávajú zvyšky p a q. Nájdite hodnotu a, ak p = 3q. Ako? Naliehavá vďaka!

odpoveď:

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

vysvetlenie:

povolania

# F_1 (x) = ax ^ 3-3x ^ 2 + 2-3 #

# F_2 (x) = ax ^ 2-5x + a #

my to vieme

# F_1 (x) = q_1 (X) (X-2) + p # a

# F_2 (x) = q_2 (X) (X-2) + q #

tak

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

# F_2 (2) = 4a-10 + e = q # a tiež

# P = 3q #

riešenie

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

získavame

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