Persaman umum akar kuadrat jika memiliki akar-akar a & b adalah

(x-a) (x-b) = x^2 - (a+b)x +ab = 0

1.

A. a=8 & b=3

a+b = 11

ab = 24

x^2 - (a+b)x +ab = 0

x^2 - 11x + 24 = 0

B. a = -4 & b =7

a+b = 3

ab = -28

x^2 - (a+b)x +ab = 0

x^2 - 3x - 28 = 0

C. a = -(1/3) & b =5

a+b = 14/3

ab = -(5/3)

x^2 - (a+b)x +ab = 0

x^2 - (14/3)x - 5/3= 0

3x^2 - 14x - 5 = 0

D. a = -(2/3) & b = 1/2

a+b = -(1/6)

ab = -(2/6)

x^2 - (a+b)x +ab = 0

x^2 - (-(1/6))x - (2/6)= 0

x^2 + (1/6)x - (2/6)= 0

6x^2 + x - 2 = 0

E. a = -1 & b = 1/5

a+b = -(4/5)

ab = -(1/5)

x^2 - (a+b)x +ab = 0

x^2 + (4/5)x - (1/5)= 0

5x^2 + 4x - 1 = 0

F. a = 1/5 & b = 1/3

a+b = 8/15

ab = 1/15

x^2 - (a+b)x +ab = 0

x^2 - (8/15)x + (1/15) = 0

15x^2 - 8x + 1 = 0

2.

3x^2 - x + 1 = 0

x^2 - (1/3)x +(1/3) = x^2 - (a+b)x +ab = 0

a+b = 1/3

ab = 1/3

Pers. Kuadrat baru yang akarnya adalah tiga lebih kecil dari akar sebelumnya.

x1 = a-3 & x2 = b-3

x1 + x2 = a+b - 6

x1. x2 = ab -3(a+b) + 9

(x-x1) (x-x2) = 0

x^2 -(x1+x2)x + x1.x2 = 0

x^2 -(a+b-6)x + (ab -3(a+b) + 9) = 0

x^2 -((1/3)-6)x + ((1/3) -3(1/3) + 9) = 0

x^2 -(-17/3)x + ((1/3) -1 +9) = 0

x^2 + (17/3)x + (25/3)= 0

3x^2 + 17x + 25 = 0

3.

2x^2 + x - 1 = 0

x^2 - (-1/2)x + (-1/2) = x^2 - (a+b)x +ab = 0

a+b = - 1/2

ab = - 1/2

Pers. Kuadrat baru yang akarnya adalah.

x1 = 2a-1 & x2 = 2b-1

x1 + x2 = 2(a+b) - 2 = 2(-1/2)-2 = - 3

x1. x2 = 4ab -2(a+b) + 1 = 4(-1/2) -2(-1/2) + 1 = -2 + 1 + 1 = 0

(x-x1) (x-x2) = 0

x^2 -(x1+x2)x + x1.x2 = 0

x^2 -(-3)x + 0 = 0

x^2 + 3x = 0