Question

If $2+3i$ is one of the roots of the equation $2x^3-9x^2+kx-13=0$, $k\in R,$ then the real root of this equation :

• A. does not exist
• B. exists and is equal to $\frac{1}{2}$
• C. exists and is equal to — $\frac{1}{2}$
• D. exists and is equal to 1

Answer 1

Answer: (B)

$\alpha =2+3i;\beta =2-3i,\gamma =?$
$\alpha \beta \gamma =\frac{13}{2}$ [since product of roots $=\frac{d}{a}$]
$\Rightarrow \left(4+9\gamma \right)=\frac{13}{2}$
$\Rightarrow \gamma =\frac{1}{2}$