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Q.
The product of two of the four roots of the equation $x^{4}-18x^{3}+kx^{2}+200x-1984=0$ is $-32,$ then the value of $k$ is
NTA AbhyasNTA Abhyas 2022
Solution:
Let $\alpha ,\beta ,\delta$ and $\gamma $ are the roots of the equation then
$\alpha +\beta +\delta+\gamma =18,\displaystyle \sum \alpha \beta =k$
$\displaystyle \sum \alpha \beta \delta=-200,\alpha \beta \delta\gamma =-1984$
Solving all, we get $k=86$