Q. If $f\left(x\right), \, g\left(x\right)\&h\left(x\right)$ are second degree polynomials and $\Delta \left(x\right)=\begin{vmatrix} f\left(x\right) & g\left(x\right) & h\left(x\right) \\ f′\left(x\right) \, \, & g′\left(x\right) & h′\left(x\right) \\ f′′\left(x\right) \, & g′′\left(x\right) & h′′\left(x\right) \end{vmatrix}$ , then the degree of $\Delta \left(x\right)$ is?

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Solution:

Here, $\Delta ′\left(\right.x\left.\right)=0$
$\therefore \Delta \left(x\right)$ is a constant function.
$\therefore $ Degree of $\Delta \left(x\right)=0$

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Here, $\Delta ′\left(\right.x\left.\right)=0$ $\therefore \Delta \left(x\right)$ is a constant function. $\therefore $ Degree of $\Delta \left(x\right)=0$