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If the roots of the equaion x^4-12 x^3+c...

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

A

`-27`

B

`-54`

C

`-81`

D

`-108`

Text Solution

Verified by Experts

The correct Answer is:
D
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`
`:'alpha beta(gamma+delta)+gamma delta(alpha+beta)=-d` ltbr `:.d=-{3.3.(3+3)+3.3(3+3)}=-108`
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