The condition to be imposed on β so that (0, β) lies on or inside the triangle having sides y + 3x + 2 = 0, 3y – 2x – 5 = 0 and 4y + x – 14 = 0 is

Clearly point (0, β) lies on y-axis.Drawing the graph of the three straight lines, we see thatQ=0,72   and  P≡0,53Therefore, the point (0, β) lies on or inside ∆ABC, when53≤β≤72