Multiple choice

If $x = -1$ is a root of the equation $\begin{vmatrix} 2-x &3 & 3\ 3& 4-x&5 \ 3 & 5 & 4-x \end{vmatrix}=0$ then the other roots are

  1. 0,11

  2. 11,12

  3. 0, 12

  4. 1,11
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A Correct answer
Explanation

Expanding the determinant with x = -1: The determinant becomes |3 3 3; 3 5 5; 3 5 5|. Since two rows are identical, the determinant is 0, confirming x = -1 is a root. Solving the characteristic equation or testing the options, we find the roots are -1, 0, and 11.

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