Metode Bairstrow

mencari akar persamaan
c. y = f(x) = x^4 + 4x³ + 21x² + 4x + 20 = 0
(x² - rx + s) (b1x² + b2x + b3)

Mencari b1, b2, b3, r, s dalam table :



r = 0 ; s = -1 ; b1 = 1 ; b2 = 4 ; b3 = 20

(x² + 1) (x² + 4x + 20)

x1,2 = -b±√b²-4ac
2a

= - 4±√(4)²-4*1*20
2*1

= - 4 ± 8 i
2

X1 = -2 + 4i
X2 = -2 - 4i

Metode faktorisasi p5

mencari akar persamaan
b. y = f(x) = X5-3.5x4-8.5x3+29.75x2+14.0625x-49.21875=0
(x+a)(x^2+b1x+b0)(x^2+4x+c0)

Mencari a, b1, b0, c1, c0 dalam table :


iterasi b0 b1 a c1 c0
1 0 0 0 -3.5 -8.5
2 -1.6544118 -2.81877 -3.5000037 2.81877 1.0998743
3 12.785555 -32.766983 3.4999988 25.767001 847.52172
4 0.1249966 -0.0347729 -0.4645987 -3.00063 -10.139576
5 -2.5390737 -1.7285583 -1.9117578 0.14032 -8.7547122
6 -3.2866953 -0.9316686 -1.7105137 -0.85782 -9.0734457
7 -3.4303003 -1.4754887 -1.5813348 -0.44318 -8.5165734
8 -1.6544118 -1.2654929 -3.4931763 1.25867 -5.2765792
9 -2.6483628 -0.6269518 -3.5220768 0.64903 -5.3669631
10 -2.6767827 -0.3397704 -3.4259998 0.26577 -5.9865113


=(x-3.4259998)(x^2-0.3397704-2.6767827)(x^2+0.26577x-5.9865113)
x1 =3.4259998

(x^2-0.3397704-2.6767827)
x1,2 = -b±√b²-4ac
2a
= --0.3397704±√(-0.3397704)²-4*1*-2.6767827
2*1
=0.3397704±3.289768
Jadi 2
x2= 1.8147692
x3= -1.4749988

(x^2+0.26577x-5.9865113)
x4,5 = -b±√b²-4ac
2a
= -0.26577±√(0.26577)²-4*1*-5.9865113
2*1
= -0.26577±4.90068
2
Jadi
x4 = 1.1587275
x5 = -5.166257

Metode Faktorisasi p4

mencari akar persamaan
a. y = f(x) = x^4 - x³ - 7x² + x + 6 = 0
(x² + b1x + b0) (x² + a1x + a0)

Mencari b1, b0, a1, a0 dalam table :




bo = -1 b1 = 0 a1 = -1 a0 = -6

(x² + b1x + b0) (x² + a1x + a0)
(x² - 1) (x² - x – 6)
(x + 1) (x – 1) (x – 3) (x + 2)

Jadi x^4 - x³ - 7x² + x + 6 = 0
Menghasilkan akar-akar
x 1 = -1 x2 = 1 x3 = 3 x4 = -2

Metode Newton Raphson

mencari akar persamaan
b. y = f(x) = x³ + x² – 3x + 3 = 0
f ‘ (x) = 3x² + 2x - 3 = 0
f “ (x) = 6x + 2 = 0

misal x1 = -1, mencari x2 = x1 – (f(x1)/f’(x1))

mencari x2, x3, x4 dst dalam table :





Jadi y = f(x) = x³ + x² – 3x + 3 = 0
menghasilkan
x = 0,491669
dengan error sebesar -1,29144