\(f(x) = 0\)\( \Leftrightarrow (4x - 1)(x + 2)(3x - 5)( - 2x + 7) = 0\)\( \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{4x - 1 = 0}\\{x + 2 = 0}\\{3x - 5 = 0}\\{ - 2x + 7 = 0}\end{array}} \right.\)\( \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{x = \dfrac{1}{4}}\\{x = - 2}\\{x = \dfrac{5}{3}}\\{x = \dfrac{7}{2}}\end{array}} \right.\)
Ta có bảng xét dấu
Từ bảng xét dấu ta thấy:
\(f(x) > 0\) khi \(x \in ( - 2;\dfrac{1}{4})\) hoặc \(x \in (\dfrac{5}{3};\dfrac{7}{2})\)
\(f(x) < 0\) khi \(x \in ( - \infty ; - 2),x \in (\dfrac{1}{4};\dfrac{5}{3}),x \in (\dfrac{7}{2}; + \infty )\)
\(f(x) = 0\)khi \(x = - 2,x = \dfrac{1}{4},x = \dfrac{5}{3},x = \dfrac{7}{2}\)
