Xét dấu các biểu thức bậc hai a;f(x) = x^2 -5x+4 b;f(x) = (x^2-2x)(x^2 +x-2)

`a)f(x)=x^2-5x+4`

Xét `x^2-5x+4=0`

  ⇔$\left[ \begin{array}{l}x=4\\x=1\end{array} \right.$ 

BXD:

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

`KL:@ f(x) > 0<=>x \in (-oo;1)uu(4;+oo)`

     `@ f(x) < 0<=>x \in (1;4)`

     `@ f(x) = 0<=>x = {1;4}`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`b)f(x)=(x^2-2x)(x^2+x-2)`

Xét `x^2-2x=0⇔`$\left[ \begin{array}{l}x=0\\x=2\end{array} \right.$ 

      `x^2+x-2=0⇔`$\left[ \begin{array}{l}x=1\\x=-2\end{array} \right.$

BXD:

$$\begin{array}{|c|cc|}\hline x&-\infty & &-2&&0&&1&&2&&+\infty&\\\hline x^2-2x & &+ & |&+&0&-&|&-&0&+&&\\\hline x^2+x-2& & + &0&-&|&-&0&+&|&+&&\\\hline f(x)&&+&0&-&0&+&0&-&0&+\\\hline\end{array}$$

`KL:@ f(x) > 0<=>x \in (-oo;-2)uu(0;1)uu(2;+oo)`

     `@ f(x) < 0<=>x \in (-2;0)uu(1;2)`

     `@ f(x) = 0<=>x = {-2;0;1;2}`