If \[f(x),\,\,g(x)\] and \[h(x)\] are three polynomials of degree 2 and \[\Delta (x)=\left| \begin{matrix} f(x) & g(x) & h(x) \\ f'(x) & g'(x) & h'(x) \\ f''(x) & g''(x) & h''(x) \\ \end{matrix} \right|,\]then \[\Delta (x)\] is a polynomial of degree

If \[f(x),\,\,g(x)\] and \[h(x)\] are three polynomials of degree 2 an

1.	If \[f(x),\,\,g(x)\] and \[h(x)\] are three polynomials of degree 2 and \[\Delta (x)=\left\| \begin{matrix} f(x) & g(x) & h(x) \\ f'(x) & g'(x) & h'(x) \\ f''(x) & g''(x) & h''(x) \\ \end{matrix} \right\|,\]then \[\Delta (x)\] is a polynomial of degree
A.	2
B.	3
C.	At most 2
D.	At most 3
Answer» D. At most 3

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If \[f(x),\,\,g(x)\] and \[h(x)\] are three polynomials of degree 2 and \[\Delta (x)=\left| \begin{matrix} f(x) & g(x) & h(x) \\ f'(x) & g'(x) & h'(x) \\ f''(x) & g''(x) & h''(x) \\ \end{matrix} \right|,\]then \[\Delta (x)\] is a polynomial of degree

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