Question

Tentukan akar-akar dari persamaan
[tex]\displaystyle \begin{vmatrix}x-1 & 4 & -1\\ 1 & x+2 & 1\\ 2x-4 & 4 & x-4\end{vmatrix}=0[/tex]

Answer 1

Matriks

det = 0

(x - 1)[(x + 2)(x - 4) - 1.4] - 4[1(x - 4) - 1(2x - 4)] + (-1)[1.4 - (x + 2)(2x - 4)] = 0

(x - 1)(x² - 2x - 12) - 4(-x) - (-2x² + 12) = 0

x³ - 3x² - 10x + 12 + 4x + 2x² - 12 = 0

x³ - x² - 6x = 0

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

x = 0 ; x = 3 ; x = -2

akar-akar persamaan :

x = {-2 , 0 , 3}