jika di ketahui akar akar dari persamaan kuadrat 2x^+mx+16=0 adalah alfa dan beta. jika alfa=2beta dan alfabeta posotif,maka berapakah nilai m??

Persamaan ²

2x² + mx + 16 = 0

alfa + beta = -b/a = -m/2
alfa . beta = c/a = 16/2 = 8

alfa + beta = -m/2
2beta + beta = -m/2
3beta = -m/2
6beta = -m
beta = -m/6


alfa . beta = 8
2beta.beta = 8
2beta² = 8
beta² = 4
beta = 2 (krn positif)

-m/6 = 2
-m = 12
m = -12

2x^2 + mx +16 =0
Akar2nya = alfa dan beta
[tex] \alpha = 2 \beta \\ maka \\ \alpha \beta = \frac{c}{a} \\ 2 \beta \times \beta = \frac{16}{2} \\ 2 { \beta }^{2} = 8 \\ \ { \beta }^{2} = \frac{8}{2} =4 \\ \beta = 2 \: diambil \: yg( + ) \\ \\ \alpha = 2 \beta = 2 \times 2 = 4 \\ \\ \alpha + \beta = \frac{ -b}{a} \\ 4 + 2 = \frac{ - m}{2} \\ 6 = \frac{ - m}{2} \\ - m = 6 \times 2 \\ m = - 12[/tex]