Ratkaise q 79?

Vastaus:

Vastaus on #=17.5#

Selitys:

Olkoon kuutioinen polynomi

#p (x) = x ^ 3 + bx ^ 2 + cx + d #

Sitten, #p (1) = 1 + b + c + d = 1 #, #=>#, # B + c + d = 0 #

# 2p (2) = 2 * (8 + 4b + 2c + d) = 1 #, #=>#, # 4b + 2c + d = -15 / 2 #

# 3p (3) = 3 * (27 + 9b + 3c + d) = 1 #, #=>#, # 9b + 3c + d = -80 / 3 #

Summa juuret #p (x) # on # S = -b #

Ratkaisu # B # vuonna #3# yhtälöt

# {(B + c + d = 0), (4b + 2c + d = -15 / 2), (9b + 3c + d = -80 / 3):} #

#<=>#, # {(3b + c = -15 / 2), (8b + 2c = -80 / 3):} #

#<=>#, # {(6b + 2c = -15), (8b + 2c = -80 / 3):} #

#<=>#, # {(2b = -80 / 3 + 15 = -35 / 3):} #

#<=>#, # {(B = -35 / 6):} #

Siksi, # S = 35/6 #

ja

# 3s = 35/2 = 17,5 #