Question

Diketahui akar-akar persamaan kuadrat x² + nx + n - 5 = 0 adalah x1 dan x2. Jika x1² + x2² = 13, maka tentukan nilai n!

(Plis bantu jawab pake caranya)

Answer 1

Fungsi kuadrat
ax^2 + bx + c = 0

x1 + x2 = -b/a
= -n/ 1
= -n
x1 × x2 = c/a
= n-5/ 1
= n-5

(x1 + x2)^2 = x1^2 + x2^2 + 2 × X1X2
n^2 = 13 + 2(n-5)
n^2 = 13 + 2n - 10
n^2 - 2n - 3 = 0
Faktorkan
(n-3) (n+1) = 0
n=3 // n= -1