$\begin{align*}
mx^2 + 2(m - 1)x + 4m & \geq 0 \quad \text{if} \begin{cases}
\Delta \leq 0 \\
a > 0
\end{cases}\\
\Delta & = b^2 - 4ac = \left[2(m - 1)\right]^2 - 4 \cdot m \cdot 4m = 4(m^2 - 2m + 1) - 16m^2\\
& = -12m^2 - 8m + 4 \leq 0\\
3m^2 + 2m - 1 & \geq 0\\
\Delta & = 4 + 12 = 16 \quad \text{if} \begin{cases}
m_1 = \frac{-2 + 4}{6} = \frac{1}{3} \\
m_2 = \frac{-2 - 4}{6} = -1
\end{cases}
\end{align*}$
م ج $ = \left( { - \infty , - 1} \right] \cup \left[ {\frac{1}{3}, + \infty } \right)$
$\eqalign{
& 2)m > 0 \cr
& 1 \cap 2 \cr} $
م ج $\left[ {\frac{1}{3}, + \infty } \right)$
امیرحسین مزدور 
