The total number of distinct x R for which vmatrix x & x^2 & 1+x^3 2x & 4x^2 & 1+8x^3 3x & 9x^2 & 1+27x^3 vmatrix =10 is

JEE Advanced 2016 Mathematics question

The total number of distinct for which is

Answer: 2

Solution

Split along the third column: \begin{vmatrix}x&x^2&1\\2x&4x^2&1\\3x&9x^2&1\end{vmatrix}\begin{vmatrix}x&x^2&x^3\\2x&4x^2&8x^3\\3x&9x^2&27x^3\end{vmatrix}x^3$+{vmatrix

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Question ID VK-026533