Question

If – 9 is a root of the equation $\left| \begin{matrix} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \end{matrix} \right| = 0$then the other two roots are.

• A. 2, 7
• B. – 2, 7
• C. 2, –7
• D. – 2, –7

Answer 1

Answer: (A)

2, 7

Answer 2

$\left| \begin{matrix} x & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \end{matrix} \right| = 0 \Rightarrow$ $(x + 9)\left| \begin{matrix} 1 & 1 & 1 \\ 2 & x & 2 \\ 7 & 6 & x \end{matrix} \right| = 0$,

by $R_{1} \rightarrow R_{1} + R_{2} + R_{3}$

$\Rightarrow (x + 9)\{(x^{2} - 12) - (2x - 14) + (12 - 7x)\} = 0$

$\Rightarrow (x + 9)(x^{2} - 9x + 14) = 0$

$\Rightarrow (x + 9)(x - 2)(x - 7) = 0$

Hence the other two roots are $x = 2,7$.