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

x² + ax + 5a + 3 = 0 akar akarnya α dan β
α + β = -a
α β = (5a +3)
.
α+ 2β = 3
α + β = - a
kurangkan --> β = a + 3
α + β = - a --> α + a + 3  = - a
α = - 2a - 3

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