Question

If one of the roots of $\left|\begin{array}{ccc}3& 5& x\\ 7& x& 7\\ x& 5& 3\end{array}\right|=0$ is $-10$, the other roots are

• A. $3,7$
• B. $4,7$
• C. $3,9$
• D. $3,4$

Answer 1

The correct option is A $3,7$

Given, $\left|\begin{array}{ccc}3& 5& x\\ 7& x& 7\\ x& 5& 3\end{array}\right|=0$

$\Rightarrow 3(3x-35)-5(21-7x)+x(35-x^2)=0$

$\Rightarrow 9x-105-105+35x+35x-x^3=0$

$\Rightarrow x^3-79x+210=0$

$\Rightarrow (x+10)(x-3)(x-7)=0$

$\Rightarrow x=-10,3,7$