2018-9-5 晴
一元二次不等式有以下幾種類型：
| 有兩個交點 | \begin{align}x^2-2x-3 & \lt 0\\(x-3)(x+1) & \lt 0\\-1\lt x & \lt 3\end{align} | 小於零取中間 |
| \begin{align}x^2-2x-3 & \geq 0\\(x-3)(x+1) & \geq 0\\x\leq -1或x&\geq 3\end{align} | 大於零取兩邊 | |
| \begin{align}x^2-2x-1&\geq 0\\x\leq 1-\sqrt{2}或x&\geq 1+\sqrt{2}\end{align} | $\Delta\gt 0$，用求根公式把零點求出來 | |
| 只有一個交點 | \begin{align}x^2-2x+1&\gt 0\\(x-1)^2&\gt 0\\x&\neq 1\end{align} | |
| \begin{align}x^2-2x+1&\geq 0\\(x-1)^2&\geq 0\\x&\in \mathbb{R}\end{align} | ||
| \begin{align}x^2-2x+1&\lt 0\\(x-1)^2&\lt 0\\x&\in \emptyset\end{align} | ||
| \begin{align}x^2-2x+1&\leq 0\\(x-1)^2&\leq 0\\x&=1\end{align} | ||
| 沒有交點 | \begin{align}x^2-2x+3&\lt 0\\x&\in \emptyset\end{align} | $\Delta\lt 0$，和x軸沒有交點 |
| \begin{align}x^2-2x+3&\geq 0\\x&\in \mathbb{R}\end{align} | $\Delta\lt 0$，和x軸沒有交點 |