Let $Δ=\begin{vmatrix}a+bx & c+dx & p+qx\\ax+b & cx+d & px+q\\u & v & w \end{vmatrix}= (k-x^2)\begin{vmatrix}a & c & p\\b & d & q\\u & v & w \end{vmatrix}$ then the value of k is :

1

The correct answer is Option (2) → 1

$Δ=\begin{vmatrix}a+bx & c+dx & p+qx\\ax+b & cx+d & px+q\\u & v & w \end{vmatrix}$

$R_1→R_1-xR_2$

$\begin{vmatrix}a(1-x^2)& c(1-x^2) & p(1-x^2)\\ax+b & cx+d & px+q\\u & v & w \end{vmatrix}$

$=(1-x^2)\begin{vmatrix}a& c & p\\ax+b & cx+d & px+q\\u & v & w \end{vmatrix}$

$R_2→R_2-xR_1$

$=(1-x^2)\begin{vmatrix}a& c & p\\b & d & q\\u & v & w \end{vmatrix}$

$k=1$