Question

Find the value of $k$ if product of two of the roots of the equation $x^4-37x^3+k{x}^2+808x-1984=0$ is $62$

Answer 1

Let the roots be a,b,c,d $abcd=-1984$

$ab=62$

$⟹cd=-32$

$a+b+c+d=37$

$⟹rootsare-8,2,4,31$

$k=ab+ac+ad+bc+bd+cd$

$=-16-32-248+8+62+122$

$=-104$