Question

Tolong bantu saya, besok. dikumpulkan

Answer 1

Nomor 1. 
a) x² + 8x + m = 0 maka a = 1, b= 8, dan c = m
akar-akarnya sama jika D = b² - 4ac = 0
D = b² - 4ac
0 = 8² - 4.1.m
0 = 64 - 4m
4m = 64
m = 64/4
m = 16
b) mx² - 2(m-1)x + m = 0
a = m, b = -2(m-1) = 2m - 2, dan c = m
0 = (-(2m - 2))² - 4.m.m
0 = 4m² - 8m + 4 - 4m²
0 = 4 - 8m
8m = 4
m = 1/2
c) x² - 3x + 3 = m
      x - 2
x² - 3x + 3 = mx - 2m
x² -3x - mx + 2m + 3 = 0
x² - (3+m)x + (2m + 3) = 0
a =1 ,b = -(3 + m), dan c = 2m + 3
0 = (-(3 + m))² - 4.1.(2m + 3)
0 = m² + 6m + 9 - 4(2m + 3)
0 = m² + 6m + 9 - 8m - 12
0 = m² -2m -3
(m - 3) (m + 1) = 0
m = 3 atau m = -1
nomor 2
kx² + 2x + k = 0 maka a = k, b = 2, dan c = k
a) akar sama D = 0
0 = 2² - 4.k.k
0 = 4 - 4k²
4k² = 4
k² = 1
k = 1
b) dua akar real maka D > 0
0 < 4 - 4k²
4 - 4k² > 0
-4k² > -4
k² < 1
-2 < k < 1 
c) akar imaginer D < 0
0 > 4 - 4k²
4 - 4k² < 0
-4k² < -4
k² > 1
k > 1