Question

Let for i = 1, 2, 3, $p_i(x)$ be a polynomial of degree 2 in x, $p_i^{\prime }(x)$ and $p_i^{\prime \prime }(x)$ be the first and second order derivatives of $p_i(x)$ respectively. Let,
$A\left(x\right)=\left[\begin{array}{ccc}{p}_1\left(x\right)& p_1^{\prime }\left(x\right)& p_1^{\prime \prime }\left(x\right)\\ p_2\left(x\right)& p_2^{\prime }\left(x\right)& p_2^{\prime \prime }\left(x\right)\\ p_3\left(x\right)& p_3^{\prime }\left(x\right)& p_3^{\prime \prime }\left(x\right)\end{array}\right]$ and $B\left(x\right)={\left[A\left(x\right)\right]}^{T}A\left(x\right)$. Then determinant of $B\left(x\right)$ :

• 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

Answer 1

Answer: (A)

Correct answer is (a) is a polynomial of degree 6 in x