Persamaan kuadrat x2 + ax + 5a + 3 = 0 mempunyai akar real α dan β. Jika α + 2β = 3, nilai konstanta a adalah..

Bab Persamaan Kuadrat
Matematika SMP Kelas VIII

α + 2β = 3
α = 3 - 2β

x² + ax + 5a + 3 = 0
p = 1; q = a; r = 5a + 3

α + β = -q/p
(3 - 2β) + β = -a/1
3 - β = -a
β = a + 3

α . β = c/a
(3 - 2β) . β = (5a + 3)/1
(3 - 2(a + 3)) . (a + 3) = 5a + 3
(3 - 2a - 6) (a + 3) = 5a + 3
(-3 - 2a) (a + 3) = 5a + 3
-3a - 9 - 2a² - 6a = 5a + 3
2a² + 9a + 5a + 3 + 9 = 0
2a² + 14a + 12 = 0
a² + 7a + 6 = 0
(a + 6) (a + 1) = 0
a = -6 atau a = -1