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Zadatak 0916

Test: MDsIVBGI_166

 

Odredi nule i znak funkcije \(y=\frac{x^2+3x-3}{x-1}\).

 

Rešenje:


$$\frac{x^2+3x-3}{x-1}=0$$
$$\Leftrightarrow x^2+3x-3=0\wedge x-1\neq 0$$
$$x_{1,2}=\frac{-3\pm \sqrt{9-4\cdot (-3)}}{2}$$
$$x_1=\frac{-3+ \sqrt{21}}{2}\approx 0,7,x_2=\frac{-3- \sqrt{21}}{2}\approx -3,7$$
$$N_1=(\frac{-3+ \sqrt{21}}{2},0), N_2=(\frac{-3- \sqrt{21}}{2},0)$$

 
\(x-x_1\)
\(x-x_2\)
\(x-1\)
\(y\)
\((-\infty \leftarrow \rightarrow x_2)\)
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---
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\((x_2 \leftarrow \rightarrow x_1)\)
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+++
---
+++
\((x_1 \leftarrow \rightarrow 1)\)
+++
+++
---
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\((1 \leftarrow \rightarrow +\infty )\)
+++
+++
+++
+++

$$y<0 \text { za }x\in \left ( -\infty ,\frac{-3- \sqrt{21}}{2} \right )\cup \left ( \frac{-3+ \sqrt{21}}{2},1 \right )$$
$$y>0 \text { za }x\in \left ( \frac{-3- \sqrt{21}}{2},\frac{-3+ \sqrt{21}}{2} \right )\cup \left ( 1,+\infty  \right )$$


 

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