Question

If $\left|\begin{array}{ccc}{x}^2-2x+3& 7x+2& x+4\\ 2x+7& x^2-x+2& 3x\\ 3& 2x-1& x^2-4x+7\end{array}\right|=a{x}^6+b{x}^5+c{x}^4+d{x}^3+e{x}^2+fx+g$ the value of $g$ is

• A. $2$
• B. $1$
• C. $-204$
• D. $-108$

Answer 1

Answer: (D)

$-108$

Put $x=0$ in the quin equation $\Rightarrow$

$\therefore \left|\begin{array}{ccc}3& 2& 4\\ 7& 2& 0\\ 3& -1& 7\end{array}\right|=g$

$4(-7-6)+7(6-14)=g$

$-52-56=g$

$g=-108$