Question

The value of the determinant $\left|\begin{array}{ccc}x+1& x+2& x+4\\ x+3& x+5& x+8\\ x+7& x+10& x+14\end{array}\right|$

• A. -2
• B. $x^2$
• C. 2
• D. x + 2

Answer 1

The correct option is A -2

$\left|\begin{array}{ccc}x+1& x+2& x+4\\ x+3& x+5& x+8\\ x+7& x+10& x+14\end{array}\right|$

$\Rightarrow R_2\to R_2-R_1,R_3\to R_3-R_1$

$\Rightarrow \left|\begin{array}{ccc}x+1& x+2& x+4\\ 2& 3& 4\\ 6& 8& 10\end{array}\right|$

$=(30-32)x+1-(20-24)(x+2)+(16-18)x+4$

$=-2x-2+4x+8-2x-8$

$=-2$

Option A is correct