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 $=\frac{d}{a}$]
$\Rightarrow \left(4+9 \,\gamma\right) = \frac{13}{2}$
$\Rightarrow \gamma = \frac{1}{2}$