If (begin{vmatrix} 1+2x & -1 \ 6 & 3-x end{vmatrix} = -3 ), find the values of x.
-
A.
(x = 3, -2) -
B.
(x = 4, frac{-2}{3}) -
C.
(x = -4, frac{3}{2}) -
D.
(x = 4, frac{-3}{2})
Correct Answer: Option D
Explanation
(begin{vmatrix} 1+2x & -1 \ 6 & 3-x end{vmatrix} = -3 implies (1+2x)(3-x) – (-6) = -3)
(3 – x + 6x – 2x^{2} + 6 = -3)
(-2x^{2} + 5x + 3 + 6 + 3 = 0)
Multiplying through with -1,
(2x^{2} – 5x -12 = 0)
((2x + 3)(x – 4) = 0 implies x = frac{-3}{2} , 4)