matematika

1. persamaan kuadrat yang akar-akarnya 3 kurang dari akar-akar persamaan kuadrat
    6X^2 - 11X + 10 =0

2. persamaan kuadrat yg akar-akarnya kebalikan dari akar-akar persamaan 2X^2 + 4X - 3 = 0

Jawab:

1.] 6x² - 11x + 10 = 0
misal akar-akarnya adalah p dan q
p + q = -b/a = 11/6
pq = c/a = 10/6

p' = p - 3 ; p = p' + 3
q' = q - 3 ; q = q' + 3

substitusi :
-> p + q = 11/6
p' + 3 + q' + 3 = 11/6
p' + q' = 11/6 - 36/6
p' + q' = -25/6

-> pq = 10/6
(p' + 3) (q' + 3) = 10/6
p'q' + 3 (p' + q') + 9 = 10/6
p'q' + 3 . -25/6 = 10/6 - 54/6
p'q' = -44/6 + 25/2
p'q' = 31/6

masukkan :
x² - (p' + q') x + p'q' = 0
x² + 25/6 x + 31/6 = 0
____________________ . 6
6x² + 25x + 31 = 0

2.] 2x² + 4x - 3 = 0
misal akar-akarnya adalah m dan n
m + n = -b/a = -4/2 = -2
mn = c/a = -3/2

m' = 1/m ; m = 1/m'
n' = 1/n ; n = 1/n'

substitusi :
-> mn = -3/2
1 / m'n' = -3/2
m'n' = -2/3

-> m + n = -2
1/m' + 1/n' = -2
[m' + n'] / m'n' = -2
m' + n' = -2 . -2/3
m' + n' = 4/3

masukkan :
x² - (m' + n') x + m'n' = 0
x² - 4/3 x - 2/3 = 0
_____________________ . 3
3x² - 4x - 2 = 0