Explanation

(c)
Given equations are $2x^{2} + 3x + 5\lambda = 0\ and\ x^{2} + 2x + 3\lambda = 0$ have a common root, if $\ \frac{x^{2}}{(9 - 10)\lambda} = \frac{x}{(5 - 6)\lambda} = \frac{1}{(4 - 3)}$
$\Rightarrow \ \frac{x^{2}}{- \lambda} = \frac{x}{- \lambda} = \frac{1}{1}$
$\Rightarrow x^{2} = - \lambda,\ x = - \lambda\ or\ \lambda = - 1,\ 0$