If $f(x)=\begin{vmatrix}a&-1&0\\

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Determinants

Question:

If $f(x)=\begin{vmatrix}a&-1&0\\ax&a&-1\\ax^2&ax&a\end{vmatrix}$, then $f(2x) - f(x)$ equals

Options:

$a (2a + 3x)$

$ax (2x + 3a)$

$ax (2a + 3x)$

$x (2a + 3x)$

Correct Answer:

$ax (2a + 3x)$

Explanation:

Applying $R_2 → R_2 -xR_1$ and $R_3 → R_3 -xR_2$, we get

$f(x)=\begin{vmatrix}a&-1&0\\0&a+x&-1\\0&0&a+x\end{vmatrix}=a(a+x)^2$

$∴f(2x)-f(x)=a(a+2x)^2-a(a+x)^2=ax(2a + 3x)$