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JEE Advanced Mathematics question

MathematicsDeterminantsJEE Advanced

Using the factor theorem it is found that , and are three factors of the determinant

.

The other factor in the value of the determinant is

Answer: (A)

Solution

Every entry is homogeneous of degree 1 in , so the determinant is a homogeneous polynomial of degree 3. The product already has degree 3, so the remaining factor is a constant :

Δ = k (b+c)(c+a)(a+b).

To f

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Question ID VK-108274