Question

Salah satu akar persamaan kuadrat x²-5x+3m=0 adalah dua kali salah satu akar persamaan kuadrat x²+x-m=0, tentukan nilai m

Answer 1

X1=2 x3

x1+x2=5 ..... x2=5 - x1
x1.x2=3m ......x1(5-x1)=3m ..... 2 x3(5 - 2 x3)=3m ...... x3(5-2 x3)=3/2 m ... (1)

x3+x4=-1 .... x4=-1 - x3
x3 . x4= - m ...... x3 (-1 - x3)= -m .... (2)

(1)dibagi (2) = (-1 -x3)/(5-2 x3)= -3/2

-1 - x3 = -3/2(5-2 x3)
-1 -x3= -15/2 + 3 x3

15/2-1= 4 x3

13/2=4x3.... x3= 13/8

(2).....13/8(-1 -13/8)= - M...M= 13/8 + (13/8)²

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