Question

If $x$ is a non-real cube root of $-2$, then the value of
$\left|\begin{array}{ccc}1& 2x& 1\\ x^2& 1& 3x^2\\ 2& 2x& 1\end{array}\right|$ equals to

• A. $-7$
• B. $-13$
• C. $0$
• D. $-12$

Answer 1

Answer: (B)

$-13$

Given, $x=\sqrt[3]{3-2}$

$\Rightarrow x^3=-2$
$\left|\begin{array}{ccc}1& 2x& 1\\ x^2& 1& 3x^2\\ 2& 2x& 1\end{array}\right|$
$=(1-6x^3)-2x(-5x^2)+1(2x^3-2)$

$=13-20-6$

$=-13$