Question

Nomor 1 dan 2 mohon jawaban dan penjelasan konsep

Answer 1

Verified answer

1) misal x^2 + 3x = p
x^2 + 3x + 2 = 2/(x^2 + 3x + 3)
p + 2 = 2/(p + 3)
(p + 2)(p + 3) = 2
p^2 + 5p + 6 = 2
p^2 + 5p + 4 = 0
(p + 4)(p + 1) = 0
p = -4 atau p = -1

p = -4 => x^2 + 3x = -4
=> x^2 + 3x + 4 = 0 => D = b^2 - 4ac = 3^2 - 4(1)(4) = 9 - 16 = -7
=> D < 0 berarti akar-akarnya tidak real

p = -1 => x^2 + 3x = -1
=> x^2 + 3x + 1 = 0 => D = b^2 - 4ac = 3^2 - 4(1)(1) = 9 - 4 = 5
=> D > a berarti akar-akarnya real berbeda
a.b = x1.x2 = c/a = 1/1 = 1

2) y = ax^2 + bx + c menyinggung y = x
y = y
ax^2 + bx + c = x
ax^2 + (b - 1)x + c = 0
Menyinggung => D = 0
b^2 - 4ac = 0
(b - 1)^2 - 4ac = 0
b^2 - 2b + 1 = 4ac

y = ax^2 + bx + c tidak menyinggung dan tidak memotong sumbu x
D < 0
b^2 - 4ac < 0
b^2 - (b^2 - 2b + 1) < 0
b^2 - b^2 + 2b - 1 < 0
2b < 1
b < 1/2