Let the roots of the equation are .Given that .From the equation Also …...........(1)….............(2)Also ….......(3)Use (1) and (3) to find .Use the values in (2) to find the value of k .Hope that clears your doubt.

Grade 12Algebra

plz find value of k?

Bevkoof Singh

11 Years agoGrade 12

1 Answer

Satyajit Samal

11 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.