1. Tardigrade
  2. Question
  3. Mathematics
  4. Let for i = 1, 2, 3, pi(x) be a polynomial of degree 2 in x, p'i(x) and p''i(x) be the first and second order derivatives of pi(x) respectively. Let, A(x) = [p1(x)&p1'(x)&p1''(x) p2(x)&p2'(x)&p2''(x) p3(x)&p3'(x)&p3''(x)] and B(x)=[A(x)]TA(x). Then determinant of B(x) :

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

Determinants

Solution:

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