JEE-Advanced 2015 (10/40)

Algebra Level 4

\[\left| \begin{array}{} (1+\alpha)^2 & (1+2\alpha)^2 & (1+3\alpha)^2 \\ (2+\alpha)^2 & (2+2\alpha)^2 & (2+3\alpha)^2 \\ (3+\alpha)^2 & (3+2\alpha)^2 & (3+3\alpha)^2 \\ \end{array} \right|=-648\alpha\]
Which of the following values of \(\alpha\) satisfy the above equation ?
\[\begin{array}{} (1) \, -4 \quad \quad \quad \quad & (2) \, 9 \\ (3) \, -9 & (4) \, 4 \end{array}\]
Note :

  • Submit your answer as the increasing order of the serial numbers of all the correct options.

  • For eg, if your answer is \((1),(2)\), then submit 12 as the correct answer, if your answer is \((2),(3),(4)\), then submit 234 as the correct answer.

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