Question

Persamaan kuardat 2x²- x - 3 = 0 Tentukan
a. X1 + X2
b. X1 × X2
c. [tex] \frac{1}{x1} + \frac{1}{x2} [/tex]
d. X1² + X2²​

Answer 1

2x² - x - 3 = 0

2x² - 3x + 2x - 3 = 0

x(2x - 3) + (2x - 3) = 0

(2x - 3)(x + 1) = 0

2x - 3 = 0 atau x + 1 = 0

2x - 3 = 0 x + 1 = 0

2x = 0 + 3 x = 0 - 1

2x = 3 x = -1

x = 2/3

maka nilai x1 = -1

x2 = 2/3

maka :

x1 + x2 :

= -1 + 2/3

= (-1 + 2)/3

= -1/3

x1 × x2

= -1 × 2/3

= (-1 × 2)/3

= -2/3

1/x1 + 1/x2 :

= 1/-1 + 1/2/3

= -1 + 1/2/3

= -1 + 2/3

= -2/2 + 3/2

= (-2 + 3)/2

= 1/2

x1² + x2²

= -1² + 2/3²

= -1 + 4/9

= (-9 + 4)/9

= -5/9

= - 5/9