Question

Xét dấu các biểu thức sau :

                 \(f\left(x\right)=\left(4x-1\right)\left(x+2\right)\left(3x-5\right)\left(-2x+7\right)\)

Answer 1

Xét:
\(4x-1=0\Leftrightarrow x=\dfrac{1}{4}\); \(x+2=0\Leftrightarrow x=-2\);
\(3x-5=0\Leftrightarrow x=\dfrac{5}{3}\); \(-2x+7=0\Leftrightarrow x=\dfrac{7}{2}\).

Vậy: \(f\left(x\right)=0\) khi \(x=\left\{-2;-\dfrac{1}{4};\dfrac{5}{3};\dfrac{7}{2}\right\}\).
\(f\left(x\right)>0\) khi \(\left(-2;-\dfrac{1}{4}\right)\cup\left(\dfrac{5}{3};\dfrac{7}{2}\right)\).
\(f\left(x\right)< 0\) khi \(\left(-\infty;-2\right)\cup\left(-\dfrac{1}{4};\dfrac{5}{3}\right)\cup\left(\dfrac{7}{2};+\infty\right)\).