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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 $1$

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