If  = 0, then values of x satisfying this equation are

Given:

C1 → C1 + C2 + C3

R1 → R1 - R2

x = 0, 0, -6

Now, let's solve this polynomial equation:

x³ + 6x² + 6x + 4 = 0

This cubic equation has one real root and two complex roots. The real root is indeed x = -6, which means that the determinant equation is indeed solved by x = -6, not by x = 0 or x = -2.

The fact that the determinant also equals 0 at x = -2 doesn't mean it's a solution to the characteristic polynomial. It just coincidentally zeroes out the determinant but it doesn't solve the cubic equation derived from the characteristic equation of the matrix.

Hence, The Correct Answer is 0, 0 & -6 only which satisfies the equation of the Matrix