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If alpha,beta,gamma are roots of equatio...

If `alpha,beta,gamma` are roots of equation `x^3-6x^2+10x-3=0` then find equation with roots `2alpha+1, 2beta+1, 2gamma+1`

A

`a + b + c = 25`

B

`a - b + c = -159`

C

`-a - b -c = 25`

D

`a + b - c = 129`

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
Let `2alpha + 1 = x rArr alpha = (x - 1)/(2)`
`((x-1)/(2))^(3) -6((x-1)/(2))^(2) + 10 ((x-1)/(2)) -3 = 0`
`x^(3) - 1 - 3x^(2) + 3x - 12(x^(2) - 2x + 1) + 40(x - 1) - 24 = 0`
`x^(3) - 15x^(2) + 67x - 77 = 0`
`a = 15`
`b = 67`
`c = -77`
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