Question

3. Jika suku banyak f ( x ) = x - x³ + ax² + x + b mempunyai faktor ( x − 3 ) dan ( x - 1 ) . Tentukan :
a. Nilai a dan b
b. Akar - akar dari f ( x )​

Answer 1

Jawab:

Penjelasan dengan langkah-langkah:

f(x) = x⁴ - x³ + ax² + x + b

x - 3 = 0

x = 3

f(3) = 0

x - 1 = 0

x = 1

f(1) = 0

f(3) = 3⁴ - 3³ + a(3)² + 3 + b

0 = 81 - 27 + 9a + 3 + b

9a + b = 27 - 81 - 3

9a + b = -57

f(1) = 1⁴ - 1³ + a(1)² + 1 + b

0 = 1 - 1 + a + 1 + b

a + b = -1

9a + b = -57

a + b = -1

a = -1 - b

9(-1 - b) + b = -57

-9 - 9b + b = -57

-8b = -57 + 9

-8b = -48

b = -48/(-8)

b = 6

a = -1 - 6

a = -7

f(x) = x⁴ - x³ - 7x² + x + 6

f(x) = (x + 1) (x + 2) (x - 3) (x - 1)

x + 1 = 0

x = -1

x + 2 = 0

x = -2

x - 1 = 0

x = 1

x - 3 = 0

x = 3

Akar-akar dari f(x) adalah x1 = -2, x2 = -1, x3 = 1, x4 = 3.