Question

Suku banyak f(x) =2x³+ax²+bx-5 dibagi oleh x²-x-2 bersisa 3x+2. nilai a+b adalah

Answer 1

X² - x - 2 = 0
(x-2)(x+1)
x1 = 2 ; x2 = -1
S(x) = 3x + 2
S(2) = 8
S(-1) = -1

S(x) = f(x)
S(x) = 2x^3 +ax^2 + bx - 5
S(2) = 16 + 4a + 2b - 5
8 = 4a + 2b + 11
4a + 2b = -3

S(-1) = -2 + a - b - 5
-1 = a - b - 7
a - b = 6

a - b = 6
4a + 2b = -5
-------------------
2a - 2b = 12
4a + 2b = -3
-------------------- +
6a = 9
a = 9/6

a - b = 6
9/6 - b = 6
b = 9/6 - 6
b = (9-36)/6
b = -27/6

a + b = 9/6 + (-27/6)
a + b = 9/6 - 27/6
a + b = -18/6
a + b = -3