A) 5
B) 25
C) 80
D) 100
Correct Answer: C
Solution :
| Let \[\alpha ,\beta ,\gamma ,\delta \]be the four positive roots then\[\alpha +\beta +\gamma +\delta =-p,\] |
| \[\alpha \beta +\beta \gamma +\gamma \delta +\alpha \gamma +\alpha \delta +\beta \delta =q,\] |
| \[\alpha \beta \gamma +\alpha \beta \delta +\alpha \gamma \delta +\beta \gamma \delta =-r\,and\,\alpha \beta \gamma \delta =5\] |
| Now \[\begin{align} & \left( \frac{\alpha +\beta +\gamma +\delta }{4} \right)\left( \frac{\alpha \beta \gamma +\alpha \beta \delta +\alpha \gamma \delta +\beta \gamma \delta }{4} \right) \\ & \\ \end{align}\] |
| \[\ge \sqrt[4]{\alpha \beta \gamma \delta }\sqrt[4]{{{\alpha }^{3}}{{\beta }^{3}}{{\gamma }^{3}}{{\delta }^{3}}}\]\[\Rightarrow \left( \frac{-p}{4} \right)\left( \frac{-r}{4} \right)\ge 5\Rightarrow pr\ge 80\]\ |
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