xét dấu biểu thức sau f(x)=(x+3)(1-4x)(2x+5)

Đáp án:

`f(x)=(x+3).(1-4x).(2x+5)`

Xét       `x + 3 = 0 <=> x = -3`

             `1 - 4x = 0 <=> x = 1/4`

             `2x + 5 = 0 <=> x = (-5)/2`

BXD:

        $$\begin{array}{|c|cc|}\hline x&-\infty & &\dfrac{-5}{2}&&-3&&\dfrac{1}{4}&&+\infty&&&\\\hline2x + 5& &- &0&+&|&+&|&+&&&&\\\hline x + 3& & -&| &-&0&+&|&+&&&&\\\hline 1 - 4x& & +&| &+&|&+&0&-&&&&\\\hline f(x)&&+&0&-&0&+&0&-&\\\hline\end{array}$$

`-> f(x) >= 0 -> x ∈ (-3; 1/4)`

     `f(x) ≤ 0 -> x ∈ (-\infty; (-5)/2) ∪ ((-5)/2; -3)  ∪ (1/4; +\infty)`

     `f(x) = 0 -> x ∈ {-3; 1/4; (-5)/2}`

`#dariana`