Description for Correct answer:
Roots of the equation \( \Large 2x^{2}+3x+5=0 \)

\( \Large x = \frac{-3\pm \sqrt{9-40}}{6} \)( imaginary roots).

Hence, both roots coincide, so on comparing

\( \Large \frac{a}{2}=\frac{b}{3}=\frac{c}{5}=K \)

=> \( \Large a=2K,\ b=3K,\ c=5K \)

=> \( \Large a+b+c = 10K \)

So, maximum value does not exist.