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Q.

If roots is of the equation x4−12x3+cx2+dx+81=0 are positiveThe value of c isThe value of d is Root of the equation 2cx + d =0, is

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a

-27

b

27

c

-54

d

54

e

-27

f

-54

g

-81

h

-108

i

-1

j

-12

k

1

l

12

answer is , , .

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Detailed Solution

c=(α+β)(γ+δ)+αβ+γδ =(3+3)(3+3)+3⋅3+3⋅3=36+18=54 ∵αβ(γ+δ)+γδ(α+β)=−d ∴ d=−{3⋅3⋅(3+3)+3⋅3⋅(3+3)}=−108Required root =−d2c=−(−108)2×54=1
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