Multiple choice

The root of the equation $\left| {\begin{array}{*{20}{c}}{3 - x} & { - 6} & 3\{ - 6} & {3 - x} & 3\3 & 3 & { - 6 - x}\end{array}} \right|$ = 0 is

  1. $6$
  2. $9$
  3. $0$

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The determinant of the matrix is (3-x)((3-x)(-6-x) - 9) + 6(-6(-6-x) - 9) + 3(-18 - 3(3-x)) = 0. Solving this cubic equation for x yields roots including 9.

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