Question

Given that x = -9 is a root of $\left|\begin{array}{ccc}x& 3& 7\\ 2& x& 2\\ 7& 6& x\end{array}\right|=0$, the other two roots are . . . and . . . .

• A. 2
• B. 8
• C. -5
• D. 7

Answer 1

Answer: (A), (D)

7

Given, $\left|\begin{array}{ccc}x& 3& 7\\ 2& x& 2\\ 7& 6& x\end{array}\right|=0$
Applying $R_1\to R_1+R_2+R_3$
$\Rightarrow \left|\begin{array}{ccc}x+9& x+9& x+9\\ 2& x& 2\\ 7& 6& x\end{array}\right|=0\Rightarrow (x+9)\left|\begin{array}{ccc}1& 1& 1\\ 2& x& 2\\ 7& 6& x\end{array}\right|=0$
Applying $C_2\to C_2-C_{1}and{C}_3\to C_3-C_1$
$\Rightarrow (x+9)\left|\begin{array}{ccc}1& 0& 0\\ 2& x-2& 0\\ 7& -1& x-7\end{array}\right|=0\Rightarrow (x+9)(x-2)(x-7)=0$
$\Rightarrow$ x =-9, 2, 7 are the roots.
$\therefore$ Other two roots are 2 and 7.