If the roots of the equaion `x^4-12 x^3+c x^2+dx+81=0` are positive then the value of c is The value of d is. Roots of the equation 2cx+d=0 is

Options

A. `-1`
B. `-1/2`
C. `1`
D. `1/2`

Answer

C

Explanation

Let roots be `alpha, beta, gamma, delta gt 0`. ltrgt `:.alpha +beta+gamma+delta=12` ltbr. `(alpha+beta)(gamma+delta)+alpha beta+gamma delta=c`
`alpha beta(gamma+delta)+gamma delta(alpha+beta)=-d`
`alpha beta gamma delta =81`
`:'AM=(alpha+beta+gamma+delta)/4=3`
and `GM=(alpha beta gamma delta)^(1//4)=(81)^(1//4)=(81)^(1//4)=3`
`:.AM=GM`
`impliesalpha =beta= gamma = delta =3`
Required root `=-d/(2c)=-((-108))/(2xx54)=-1`