Question

The determinant $\Delta = \begin{vmatrix} a^3+ax & ab & ac \\ a & a^2b & b^2+x & bc \\ a^2c & bc & c^2+x \end{vmatrix}$

is divisible by

• A. x
• B. x²
• C. a² + b²+c²-x
• D. a² + b²+c²+x

Answer 1

Answer: (B)

x²

Answer 2

The given determinant is likely a typo. Based on the similar question, the intended determinant is assumed to be: $\Delta = \begin{vmatrix} a^2+x & ab & ac \\ ab & b^2+x & bc \\ ac & bc & c^2+x \end{vmatrix}$ This determinant can be expressed as: $\Delta = x^2(a^2+b^2+c^2+x)$ From this expression, it is clear that $\Delta$ is divisible by $x^2$.