Akar akar persamaan kuadrat 2x² + mx + 16 = 0 adalah a dan β. Jika a = 2β dan a, β positif maka nilai m adalah . . . .

2x² + mx + 16 = 0

a,b
= [tex] \frac{-m +- \sqrt{m^2-4(2)(16)}}{2(2)} [/tex]
= [tex] \frac{-m +- \sqrt{m^2 - 128}}{4} [/tex]

a = [tex] \frac{-m + \sqrt{m^2 - 128}}{4} [/tex]
b = [tex] \frac{-m - \sqrt{m^2 - 128}}{4} [/tex]
*karna a>b*

a = 2b
[tex] \frac{-m + \sqrt{m^2 - 128}}{4} [/tex] = 2([tex] \frac{-m - \sqrt{m^2 - 128}}{4} [/tex])
[tex] \frac{m + 3\sqrt{m^2 - 128}}{4} [/tex] = 0
m + 3[tex] \sqrt{m^2 -128} [/tex] = 0
m = -3[tex] \sqrt{m^2 -128} [/tex]
m² = 9(m² -128)
m² = 9m² - 1152
0 = 8m² - 1152
0 = m² - 144
0 = (m+12)(m-12)

m = -12 atau m = 12