The product of two of the four roots of the equation x4-18x3+kx2+200x-1984=0 is -32, then the value of k is

Question

The product of two of the four roots of the equation x4-18x3+kx2+200x-1984=0 is -32, then the value of k is (A) 76 (B) 96 (C) 86 (D) 66

Tardigrade Admin · Accepted Answer

Let α ,β ,δ and &gamma; are the roots of the equation then α +β +δ+&gamma; =18, displaystyle ∑ α β =k displaystyle ∑ α β δ=-200,α β δ&gamma; =-1984 Solving all, we get k=86

Q. The product of two of the four roots of the equation $x^{4} - 18 x^{3} + k x^{2} + 200 x - 1984 = 0$ is $- 32,$ then the value of $k$ is

$76$

$96$

$86$

$66$

Let $α, β, δ$ and $γ$ are the roots of the equation then
$α + β + δ + γ = 18, \sum α β = k$
$\sum α β δ = - 200, α β δ γ = - 1984$
Solving all, we get $k = 86$

Q. The product of two of the four roots of the equation x4−18x3+kx2+200x−1984=0 is −32, then the value of k is

76

96

86

66