Question

Jika x1 dan x2 adalah akar persamaan kuadrat 2X² - 3X + 6 = 0, tentukan persamaan kuadrat berikut:
a. 1/x1 dan 1/x2
b. x1/x2 dan x1/x2
c. (x1 - 4) dan (x2 - 4)

Answer 1

Verified answer

X² - (x1 + x2)x + x1.x2 = 0
x1 + x2 = -(-3)/2 = 3/2
x1.x1 = 6/2 = 3

a) x² - (1/x1 + 1/x2)x + 1/x1 . 1/x2 = 0
x² - {(x1+x2)/x1.x2}x + 1/(x1.x2) = 0
x² - {(3/2) / 3}x + 1/3 = 0
x² - ½x + ⅓ = 0
kali dengan 6
6x² - 3x + 2 = 0

b) mungkin salah tulis soal

c) x² - (x1-4 + x2-4)x + (x1-4)(x2-4) = 0
x² - (x1+x2 - 8)x + (x1.x2 - 4(x1+x2) + 16) = 0
x² - (3/2 + 8)x + (3 - 4(3/2) + 16) = 0
x² - (19/2)x + 13 = 0
kalikan 2
2x² - 19x + 26 = 0