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4-2.Quadratic Equations and Inequations
hard
lf $2 + 3i$ 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
exists and is equal to $-\frac {1}{2}$
B
exists and is equal to $\frac {1}{2}$
C
exists and is equal to $1.$
D
does not exist.
(JEE MAIN-2015)
Solution
$\alpha=2+3 i ; \beta=2-3 i, \gamma=?$
$\alpha \beta \gamma=\frac{13}{2}\left[\text { since product of roots }=\frac{d}{a}\right]$
$\Rightarrow(4+9)=\frac{13}{2} \Rightarrow \gamma=\frac{1}{2}$
Standard 11
Mathematics
