JEE Main 2018 (Offline)Question 1
If $\begin{vmatrix}x-4&2x&2x\\2x&x-4&2x\\2x&2x&x-4\end{vmatrix}=(A+Bx)(x-A)^2$, then the ordered pair $(A,B)$ is equal to
Determinant
Solution
Adding all columns to $C_1$ gives factor $5x-4$; the remaining determinant is $(-x-4)^2$. So $\Delta=(5x-4)(x+4)^2=(A+Bx)(x-A)^2$ with $A=-4$, $B=5$.