If $f(x)=\begin{vmatrix}a&-1&0\\ax&a&-1\\ax^2&ax&a\end{vmatrix}$, then $f(2x) - f(x)$ equals
Answer & explanation
Correct answer: option 3
Applying $R_2 → R_2 -xR_1$ and $R_3 → R_3 -xR_2$, we get
$f(x)=\begin{vmatrix}a&-1&0\\0&a+x&-1\\0&0&a+x\end{vmatrix}=a(a+x)^2$
$∴f(2x)-f(x)=a(a+2x)^2-a(a+x)^2=ax(2a + 3x)$