Jika (x-2)dan(2x+1)merupakan faktor dari suku banyak 2x³+ax²+bx-2 tentukan nilai a dan b

jawab

x - 2 =0
x= 2

2x+ 1 = 0
x = - 1/2

f(x) = 2x³ + ax² + bx - 2
f(2)= 0 --> 2(8) + a(4) + b(2) - 2 = 0
16 + 4a + 2b  - 2= 0
4a  + 2b = - 14.....(i)

f(-1/2) = 0
2(-1/8) + a(1/4) +b (-1/2) - 2 = 0
-1/4  + 1/4 a - 1/2 b -2 =0
1/4 a - 1/2 b  = 9/4 ....kalikan 4
a - 2b =  9 ...(ii)


(i) dan(ii)
4a + 2b = - 14
a - 2b=  9
.........................(+)
5a = -5
a= -1

a - 2b = 9
-1 - 2b = 9
-2b = 10
b = -5

(a,b)= (1, -5)

x - 2 = 0 ---> x = 2

2x³ + ax² + bx - 2 = 0
2.2³ + a.2² + b.2 - 2 = 0
4a + 2b = 2 - 16
4a + 2b = -14 ... (1)

2x + 1 = 0 ---> x = -1/2

2.(-1/2)³ + a(-1/2)² + b(-1/2) - 2 = 0
1/4 a - 1/2 b = 2 + 1/4
Kalikan 4
a - 2b = 9 ... (2)

Jumlahkan persmaan (1) dan (2)
4a + a = -14 + 9
5a = -5
a = -1 ✔

a - 2b = 9
2b = a - 9
2b = -10
b = -5 ✔