JEE Advanced Mathematics question

MathematicsDeterminantsJEE Advanced

The determinant

\begin{vmatrix} xp+y & x & y \\ yp+z & y & z \\ 0 & xp+y & yp+z \end{vmatrix}=0

for all if

Answer: (B)

Solution

Apply : - row 1: - row 2: - row 3: 0 - p(xp+y) - (yp+z) = -(xp^2 + 2yp + z)

Δ = \begin{vmatrix} 0 & x & y \\ 0 & y & z \\ -(xp^2+2yp+z) & xp+y & yp+z \end{vmatrix} =

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Question ID VK-108251