Question

The roots of the equation $\begin{vmatrix}0&x&16\\\ x&5&7\\\ 0&9&x\end{vmatrix} = 0$ are :

• A. 0, 12 and 12
• B. 0 and $\pm$12
• C. 0, 12 and 16
• D. 0, 9 and 16

Answer 1

Answer: (B)

0 and $\pm$12

Answer 2

Given $\begin{vmatrix}0&x&16\\\ x&5&7\\\ 0&9&x\end{vmatrix} = 0$ $\Rightarrow \ 0 (5x - 63) - x (x^2 - 0) + 16 (9x - 0) = 0$ $\Rightarrow \ - x^3 + 144x = 0$ $\Rightarrow \ x (144 - x^2) = 0$ $\Rightarrow \ x = 0, \pm 12.$