Question

Tentukan akar persamaan berikut
a. 2x* - x -3=0
b. x* - x + 1/4 =0

carilah diskriminan dan himpunan selesaian

Answer 1

A. a= 2
    b = -1
    c = -3
d = b²-4ac = 1 - 4.2.-3 = 1 + 24 = 25
hp = difaktorkan.
2x² - x - 3 = 2x² + 2x - 3x - 3
               = 2x (x+1) -3(x+1)
               = (2x-3)(x+1)
2x-3 = 0
2x=3
x=3/2
x+1 = 0
x=-1
hp = {3/2 dan -1}
b. a= 1
    b = -1
    c = 1/4
d = b²-4ac = 1 - 4.1.1/4 = 1-(-1)=2
hp = difaktorkan.
x²-x+1/4=0 (kali 4 biar sama)
4x² - 4x + 1 = 0
4x² - 2x - 2x + 1 = 0
2x(2x-1) -1(2x-1) = 0
pemfaktorannya = (2x-1)(2x-1) = (2x-1)²
2x-1 = 0
2x=1
x=1/2
hp = {1/2}