Persamaan x² + qx + q – 5 = 0 , akar akarnya X1 dan X2 . Bila X1² + X2² = 13 , tentukan nilai q !
Jawaban Terkonfirmasi
X² + qx + q – 5 = 0
a = 1
b = q
c = q – 5
x1² + x2² = (x1 + x2)² – 2x1x2
= (-b/a)² – 2(c/a)
= (-q/1)² – 2((q-5)/1)
= (-q)² – 2(q – 5)
= q² – 2q + 10
q² – 2q + 10 = 13
q² – 2q + 10 – 13 = 0
q² – 2q – 3 = 0
(q – 3)(q + 1) = 0
q = 3 atau q = -1