For the line $ax+by+c=0$ to pass through the first, second, and fourth quadrants, it must have certain traits due to the positions of the axes and the quadrants:
- In the first quadrant, both $x$ and $y$ are positive.
- In the second quadrant, $x$ is negative and $y$ is positive.
- In the fourth quadrant, $x$ is positive and $y$ is negative.

For the line to be in the first and second quadrants, $by+c$ must be negative when $x$ is positive (since $ax$ is positive in the first quadrant and negative in the second quadrant). This implies that $c$ must be negative because if c were positive, then $by+c$ could never be negative when y is positive (in the first and second quadrants).

Thus, considering $c 0$ so that a negative $y$ makes $by$ negative and the entire expression negative.

From this analysis, since $c 0$ because a negative times a negative yields a positive.
- $b$ must be positive, leading to bc 0, bc<0} $