Question

Diketahui suku banyak p(x) = 2x^4 + ax^3 - 3x^2 + 5x + b. jika p(x) dibahagi (x-1) sisa 11, dibahagi (x+1) bersisa -1. Maka nilai (2a+b) adalah...

Answer 1

P(x) dibagi (x-1) sisa 11 --> p(1) = 11
p(1) = 11
2(1)⁴ + a(1)³ - 3(1)² + 5(1) + b = 11
2 + a - 3 + 5 + b = 11
a + b = 7

p(x) dibagi (x+1) sisa -1 --> p(-1) = -1
p(-1) = -1
2(-1)⁴ + a(-1)³ - 3(-1)² + 5(-1) + b = -1
2 - a - 3 - 5 + b = -1
-a + b = 5

a + b = 7
-a + b = 5
------------------------
2b = 12
b = 6

a = 1

2a + b = 2(1) + 6 = 8