Question

Bantu jawab no 6, 7 & 8

Answer 1

6. x² + (p + 1)x - 18 = 0
a = 1
b = p + 1
c = -18

α + 2β = 0
α = -2β

α . β = c/a
-2β . β = -18/1
-2β² = -18
β² = -18 : (-2)
β = √9
β = 3

α + β = -b/a
α + β = -(p + 1)/1
α + β = -p - 1
-2β + β = -p - 1
-β = -p - 1
-3 + 1 = -p
-2 = -p
p = 2

Jawaban: C

7. (m - 1)x² + 4x + 2m = 0
a = m - 1
b = 4
c = 2m

Syarat dua akar real dan berlainan:
D > 0
b² - 4ac > 0
4² - 4 . (m - 1) . 2m > 0
16 - 8m² + 8m > 0
-8m² + 8m + 16 > 0
-8m² + 16m - 8m + 16 > 0
-8m(m - 2) -8(m - 2) > 0
(m - 2)(-8m - 8) > 0

m = 2 atau m = -1

Uji titik
   ---     +++    ---
-------|--------|--------
       -1        2

Nilai m yang memenuhi: -1 < m < 2, m ≠ 1

Jawaban: A

8. x² + x - p = 0
a = 1
b = 1
c = -p

x1 + x2 = -b/a
x1 + x2 = -1/1
x1 + x2 = -1

x1 . x2 = c/a
x1 . x2 = -p/1
x1 . x2 = -p

x1/x2 + x2/x1
= (x1² + x2²)/(x1 . x2)
= [(x1 + x2)² - 2x1 . x2]/(x1 . x2)
= [(-1)² - 2 . (-p)]/(-p)
= (1 + 2p)/(-p)
= -1/p - 2 = -2 - 1/p

Jawaban: A