salah satu akar persamaan kuadrat mx2-3x+2=0 adalah dua kali akar yang lain

mx² - 3x + 2 = 0

Misalkan akar2nya [tex] x_1 [/tex] dan [tex] x_2 [/tex] sehingga
[tex] x_1 = 2x_2 [/tex]

Dari persamaan kuadrat di soal, didapat
a = m
b = -3
c = 2

[tex] x_1 + x_2 = \frac{-b}{a} \\ x_1 + x_2 = \frac{-(-3)}{m} \\ x_1 + x_2 = \frac{3}{m} \\ {*substitusi nilai x_1*} \\ 2x_2 + x_2 = \frac{3}{m} \\ 3x_2 = \frac{3}{m} \\ m = \frac{1}{x_2} [/tex]

[tex] x_1.x_2 = \frac{c}{a} \\ x_1.x_2 = \frac{2}{m} \\ 2x_2.x_2 = \frac{2}{m} \\ 2(x_2)^2 = \frac{2}{m} \\ 2(x_2)^2 = \frac{2}{\frac{1}{x_2}} \\ 2(x_2)^2 = 2x_2 \\ x_2 = 1 \\ {} \\ m = \frac{1}{x_2} \\ m = \frac{1}{1} = 1 [/tex]