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If $$f(x), g(x), h(x)$$ are three polynomials of degree $$3$$, then $$\phi(x)=\begin{vmatrix} f'(x) & g'(x) & h'(x) \\ f''(x) & g''(x) & h''(x) \\ f'''(x) & g'''(x) & h'''(x) \end{vmatrix}$$ a polynomial of degree:


A
3
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B
4
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C
5
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D
None of these
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Solution

The correct option is A 3
Writing degrees in the determinant, 
$$\begin{vmatrix} 2 & 2 & 2 \\ 1 & 1 & 1 \\ 0 & 0 & 0 \end{vmatrix}$$
Hence as we expand the determinant, we would have terms with $$x^2\times x\times \lambda$$ form, $$\Rightarrow \phi (x)$$ would be of $$3$$ degree $$\Rightarrow (A)$$

Mathematics

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