$x^{3}$ + 3$x^{2}$ + 4x + 5 = 0 ... (i)
$x^{3}$ + 2$x^{2}$ + 7x + 3 = 0 ... (ii)
Equating equations (i) and (ii), we get,
$x^{2}$ – 3x + 2 = 0
x = 1 or x = 2
Since both x = 1 and x = 2, do not satisfy either (i) or (ii), there exists no common roots for equations (i) and (ii).
Hence, option (A).0