Question

Let $A=\left|\begin{array}{cc}2& e^{i\pi }\\ i^2& i^{2012}\end{array}\right|,C=\frac{d}{dx}\left(\frac{1}{x}\right){|}_{x=1}$ and $D={\int }_{e^2}^1\frac{dx}{x}$. If the sum of two roots of the equation $A{x}^3+B{x}^2+Cx+D=0$ is equal to zero, then $B=$

• A. $-1$
• B. $0$
• C. $1$
• D. $2$

Answer 1

The correct option is D $2$

$A=1,B=?,C=-1,D=-2$

$A{x}^3+B{x}^2+Cx+D=0$

$x^3+B{x}^2-x-2=0$

$\alpha +\beta +\gamma =-B$

Sum of the roots of the equation $\alpha +\beta =0$

$\gamma =-B$

$-B^3+B^3+B-2=0$
$B=2$