Question

If -9 is a root of the equation
$$\left|\begin{array}{ccc}x& 3& 7\\ 2& x& 2\\ 7& 6& x\end{array}\right|$$=0

then the other two roots are

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

Answer 1

The correct option is A 2,7

$\left|\begin{array}{ccc}x& 3& 7\\ 2& x& 2\\ 7& 6& x\end{array}\right|=0\Rightarrow (x+9)\left|\begin{array}{ccc}1& 1& 1\\ 2& x& 2\\ 7& 6& x\end{array}\right|=0,$
by $R_1\to R_1+R_2+R_3$
$\Rightarrow (x+9)\left\{\right(x^2-12)-(2x-14)+(12-7x\left)\right\}=0\Rightarrow (x+9)(x^2-9x+14)=0\Rightarrow (x+9)(x-2)(x-7)=0$
Hence the other two roots are x=2,7.