\(f(x) = 0\)\( \Leftrightarrow ( - 2x + 3)(x - 2)(x + 4) = 0\)\( \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{ - 2x + 3}\\{x - 2}\\{x + 4}\end{array}} \right.\)\( \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{x = \dfrac{3}{2}}\\{x = 2}\\{x = - 4}\end{array}} \right.\)
Ta có bảng xét dấu
Từ bảng xét dấu ta thấy:
\(f(x) > 0\)khi \(x \in ( - \infty ; - 4)\)hoặc \(x \in (\dfrac{3}{2};2)\)
\(f(x) < 0\)khi \(x \in ( - 4;\dfrac{3}{2})\) hoặc \(x \in (2; - \infty )\)
\(f(x) = 0\) khi \(x = - 4,x = \dfrac{3}{2},x = 2\).
