If $f\left( x \right),{\rm{g}}\left( x \right)$ and $h\left( x \right)$ are three polynomials of degree 2 and ${\rm{\Delta }}\left( x \right) = \left| {\begin{array}{*{20}{c}} {f\left( x \right)}&{{\rm{g}}\left( x \right)}&{h\left( x \right)}\\ {f'\left( x \right)}&{{\rm{g'}}\left( x \right)}&{h'\left( x \right)}\\ {f''\left( x \right)}&{{\rm{g''}}\left( x \right)}&{h''\left( x \right)} \end{array}} \right|$, then ${\rm{\Delta }}\left( x \right)$ is polynomial of degree

JEE MATHEMATICS MCQ: MATRICES

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f\left( x \right),\mathrm{g}\left( x \right)

and

h\left( x \right)

are three polynomials of degree 2 and

\mathrm{\Delta }\left( x \right) = \left| {\begin{array}{cccccccccccccccccccc} {f\left( x \right)}&{\mathrm{g}\left( x \right)}&{h\left( x \right)}\\ {f'\left( x \right)}&{\mathrm{g'}\left( x \right)}&{h'\left( x \right)}\\ {f''\left( x \right)}&{\mathrm{g''}\left( x \right)}&{h''\left( x \right)} \end{array}} \right|

, then

\mathrm{\Delta }\left( x \right)

is polynomial of degree

View answer and explanation

Correct option: C

At most 2

Option C (At most 2) is correct because the determinant is a polynomial of degree at most 2 after simplification.