Question

Diketahui akar akar persamaan kuadrat 3x^2-5x-1= 0 adalah x1 dan x2. persamaan kuadrat yg akar akarnya (1/x1 +1) dan (1/x2+1) adalah..

Answer 1

3x^2 - 5x - 1 = 0
x1 + x2 = -b/a = 5/3
x1.x2 = c/a = -1/3
1/x1 + 1/x2 = (x2 + x1)/x1x2 = (5/3)/(-1/3) = -5

Misal p = 1/x1 + 1 dan q = 1/x2 + 1

p + q = 1/x1 + 1 + 1/x2 + 1 = 1/x1 + 1/x2 + 2 = -5 + 2 = -3

pq = (1/x1 + 1)(1/x2 + 1) = 1/x1x2 + 1/x1 + 1/x2 + 1
= 1/(-1/3) + (-5) + 1 = -3 - 5 + 1 = -7
Persamaan kuadrat baru
x^2 - (p + q)x + pq = 0
x^2 - (-3)x + (-7) = 0
x^2 + 3x - 7 = 0