Let for $\;i=1,2,3,p_{i}x\;$ be a polynomial of degree 2 in $\;x,p_{i}^{'}x,p_{i}^{''}x\;$ be the first and second order derivatives of $\;p_{i}x\;$ respectively . Let , $\;A(x) = \begin{bmatrix} p_{1}(x)&p_{1}^{'}(x)&p_{1}^{''}(x) \\[0.3em] p_{2}(x)&p_{2}^{'}(x)&p_{2}^{''}(x) \\[0.3em] p_{3}(x)&p_{}^{'}(x)&p_{3}^{''}(x) \end{bmatrix}\;$ and $\;B(x) =[A(x)]^{T}A(x) \;$.Then determinant of $\;B(x)\;$ :

Question

(a) is a polynomial of degree 6 in x .\[\](b) is a polynomial of degree 3 in x .\[\](c) is a polynomial of degree 2 in x .\[\](d) does not depend on x .