Point Inside Triangle Parameter 'a'

Checking the position of $(a, a^2)$ relative to origin $(0,0)$ for all three line equations: Line 1: $2x + 3y - 1 = 0$. Opposite side to origin $\implies (2a + 3a^2 - 1)(-1) < 0 \implies 3a^2 + 2a - 1 > 0 \implies a < -1$ or $a > 1/3$. Line 2: $x + 2y - 3 = 0$. Same side as origin $\implies (a + 2a^2 - 3)(-3) > 0 \implies 2a^2 + a - 3 < 0 \implies -3/2 < a < 1$. Line 3: $5x - 6y - 1 = 0$. Same side as origin $\implies (5a - 6a^2 - 1)(-1) > 0 \implies 6a^2 - 5a + 1 > 0 \implies a < 1/3$ or $a > 1/2$. Combining all three conditions yields: $a \in (-3/2, -1) \cup (1/2, 1)$.