persamaan 2x²+qx+(q-1)=0 mempunyai akar-akar x1 dan x2. jika x1²x2 + x1x2²= -5, maka nilai q?

Bab Persamaan Kuadrat
Matematika SMP Kelas VIII

2x² + qx + (q - 1) = 0
a = 2; b = q; c = q - 1

x1² x2 + x1 . x2² = - 5
x1x2 (x1 + x2) = -5
c/a . (-b/a) = -5
(q - 1)/2 . (-q/2) = -5
***dikali 4***
(q - 1) . (-q) = -20
q² - q - 20 = 0
(q - 5) (q + 4) = 0
q = 5 atau q = -4

Matematika X SMA
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Pembahasan :
2x² + qx + (q - 1) = 0

Berdasarkan Teorema Vietta
X1 + X2 = -b/a
X1 + X2 = -q/2

X1 . X2 = c/a
X1 . X2 = (q - 1)/2

Maka...
X1² . X2 + X1 . X2² = -5
X1(X1 . X2) + X2(X1 . X2) = -5
(X1 + X2)(X1 . X2) = -5
(-q/2)(q - 1)/2 = -5
(-q² + q)/4 = -5
-q² + q = -20
q² - q - 20 = 0
(q - 5)(q + 4) = 0
q = 5
q = -4