Question

If 7 and 2 are roots of equation $\left|\begin{array}{ccc}x& 3& 7\\ 2& x& 2\\ 7& 6& x\end{array}\right|=0$ then 3rd root is

• A. -9
• B. 14
• C. 1/2
• D. None of these

Answer 1

The correct option is A -9

$\left|\begin{array}{ccc}x& 3& 7\\ 2& x& 2\\ 7& 6& x\end{array}\right|=0$

$=x(x^2-12)-3(2x-14)+7(12-7x)=0$

$\Rightarrow x^3-12x-6x+42+84-49x=0$

$\Rightarrow x^3-67x+126=0$

Given:$7$ and $2$ are the roots of the equation, then $(x-7)(x-2)=x^2-9x+14=0$ is a factor of the given equation then the other root is obtained by dividing $x^3-67x+126=0$ by $x^2-9x+14=0$