Question

Kesamaan suku banyak. Tentukan nilai a, b dan c
1. 3x^2-11x+3 = a (x-2) (x-1) + b (x-1) + c
2. 6x^2-14x-27= a(x-3)^2 + b (x-2) (x-3)+c (x+2)

Answer 1

1)
3x² - 11x + 3 = a(x²- 3x + 2) + b(x-1) + c
3x² - 11x + 3 = ax² - 3ax + 2a  + bx - b + c
3x² - 11x + 3 = ax² + (-3a +b)x + (2a - b + c)
a= 3

-3a + b = -11 --> -3(3) + b = - 11
b  = -11 + 9
b = - 2

2a - b + c = 3
2(3) - (-2) + c = 3
6 + 2 + c =3
c= 3 - 8
c = - 5

(a,b,c)= (3, -2, -5)

2.
6x² - 14x - 27 = a(x-3)² + b(x-2) + c(x+2)
6x² -14x - 27 = a(x²-6x +9) + bx - 2b + cx + 2c
6x² - 14x - 27 = ax² - 6ax + 9a + bx - 2b + cx + 2c
6x² -14x - 27 = ax²+(-6a +b+c)x + (9a-2b+ 2c)
a = 6
-6a + b + c = -14
-6(6) + b + c = - 14
b + c = -14 + 36
b + c = 22 ...(1)

9a - 2b + 2c = - 27
9(6) - 2b + 2c = - 27
-2b + 2c = -27 - 54
-2b + 2c = -81
atau
b - c = 40,5.....(2)
.
(1) dan (2) eliminasikan
b + c = 22
b - c = 40,5
...............(+)
2b =62,5
b= 31,25

b- c = 22
c= b - 22
c = 31,25 - 22
c= 9,25
.
(a.b.c)=(6 ; 31,5 ;  9,25)