Question

If $5$ is one root of the equation $\left|\begin{array}{ccc}x& 3& 7\\ 2& x& -2\\ 7& 8& x\end{array}\right|=0$, then the other two roots of the equation are

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

Answer 1

The correct option is C $2,-7$

Solution:

Given that:

$5$ is a root of the equation ,

$\left|\begin{array}{ccc}x& 3& 7\\ 2& x& -2\\ 7& 8& x\end{array}\right|=0$

or, $x(x^2+16)-3(2x+14)+7(16-7x)=0$

or, $x^3+16x-42-6x+112-49x=0$

or, $x^3-39x+70=0$

If $5$ is one of the root, then

or, $(x-5)(x^2+5x-14)=0$

or, $(x-5)(x+7)(x-2)=0$

or, $x=5,$ or $x=-7$ or, $x=2$

Hence, C is the correct option.