JEE Advanced 2015 Paper 1Question 1
Which of the following values of $\alpha$ satisfy the equation $$\begin{vmatrix}(1+\alpha)^2&(1+2\alpha)^2&(1+3\alpha)^2\\(2+\alpha)^2&(2+2\alpha)^2&(2+3\alpha)^2\\(3+\alpha)^2&(3+2\alpha)^2&(3+3\alpha)^2\end{vmatrix}=-648\alpha\ ?$$
Determinant
Solution
Expanding the determinant gives $-8\alpha^3$. So $-8\alpha^3=-648\alpha$, i.e. $\alpha(\alpha^2-81)=0$, giving $\alpha=0,\pm9$; among the options $9$ and $-9$.