1. x = -5 atau x = 7

2. x = 1/5 atau x = 1/2

3. x² - 5x - 24 = 0

4. a. (-5,0) dn (7,0)

b. (0, -105)

c. (1, -108)

Penjelasan dengan langkah-langkah:

1. 1/2 x² - x - 35/2 =0 (kedua ruas x 2)

x² - 2x - 35 = 0

(x + 5)(x - 7) = 0

x + 5 = 0 atau x - 7 = 0

x = -5 x = 7

2. x² - (7/10)x + 1/10 = 0 (kedua ruas x 10)

10x² - 7x + 1 = 0

10x² - 5x - 2x + 1 = 0

5x(2x - 1) - 1(2x - 1) = 0

(2x - 1)(5x - 1) = 0

2x - 1 = 0 atau 5x - 1 = 0

2x = 1 5x = 1

x = 1/2 x = 1/5

3. (x - (-3))(x - 8) = 0

(x + 3)(x - 8) = 0

x² - 8x + 3x - 24 = 0

x² - 5x - 24 = 0

4. Y= 3x²-6x-105

a = 3, b = -6, c = -105

a. titik potong sumbu x, y = 0

3x²-6x-105 = 0 (kedua ruas dibagi 3)

x² - 2x - 35 = 0

(x + 5)(x - 7) = 0

x + 5 = 0 atau x - 7 = 0

x = -5 x = 7

titik potong (-5,0) dn (7,0)

b. titik potong sumbu y, (0, c)

maka titik potongnya (0, -105)

c. - sumbu simetri

x = -b/2a

= -(-6)/2.3

= 6/6

= 1

- y optimal

y = 3.1² - 6.1 - 105

= 3 - 6 - 105

= -108

- titik puncak minimumnya

(1, -108)