If the equations `x^2+2x+3lambda=0` and `2x^2+3x+5lambda=0` have a non-zero common roots, then `lambda=` (a) `1` (b) `-1` (c) `3` (d) none of these

Explanation

To solve the problem, we need to find the value of \( \lambda \) such that the equations \( x^2 + 2x + 3\lambda = 0 \) and \( 2x^2 + 3x + 5\lambda = 0 \) have a non-zero common root.

### Step-by-Step Solution:

1. **Let the common root be \( c \)**:
Since \( c \) is a common root, it must satisfy both equations:
\[
c^2 + 2c + 3\lambda = 0 \quad \text{(1)}
...