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plz find value of k?

plz find value of k?

Question Image
Grade:12

1 Answers

Satyajit Samal
askIITians Faculty 34 Points
7 years ago
Let the roots of the equation are r_{1}, r_{2},r_{3}\; and\; r_{4} .
Given that r_{1} \times r_{2} = -31 .
From the equation r_{1} \times r_{2} \times r_{3} \times r_{4}=-2015 \\ \Rightarrow r_{3}\times r_{4} = 65
Also \left (r_{1}+r_{2} \right )+\left (r_{3}+r_{4} \right )=18 …...........(1)
\sum r_{1}r_{2} = k \\ \Rightarrow \left ( r_{1}+r_{2} \right )\left ( r_{3}+r_{4} \right ) + r_{1}r_{2}+r_{3}r_{4}=k….............(2)
Also \sum r_{1}r_{2}r_{3}= -174 \\ \Rightarrow r_{1}r_{2}\left ( r_{3}+r_{4} \right ) + r_{3}r_{4}\left ( r_{1}+r_{2} \right ) = -174 ….......(3)
Use (1) and (3) to find \left (r_{1}+r_{2} \right )] and [\left (r_{3}+r_{4} \right ) .
Use the values in (2) to find the value of k .
Hope that clears your doubt.

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