Let `|(x^2+3x,x-1,x+3),(x+1,-2x x-4),(x-3,x+4 ,3x)|=a x^4+b x^3+c x^2+e` be an identity in `x ,` where `a , b , c , d , e` are independent of `xdot` Then the value of `e` is 4 (b) 0 (c) 1 (d) none of these

Explanation

To solve the problem, we need to evaluate the determinant given in the question and find the constant term \( e \) when \( x = 0 \).

The determinant is given as:

\[
D = \begin{vmatrix}
x^2 + 3x & x - 1 & x + 3 \\
x + 1 & -2x & x - 4 \\
...