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If alphaa n dbeta are roots of the equat...

If `alphaa n dbeta` are roots of the equation `a x^2+b x+c=0,` then the roots of the equation `a(2x+1)^2-b(2x+1)(3-x)+c(3-x)^2=0` are `(2alpha+1)/(alpha-3),(2beta+1)/(beta-3)` b. `(3alpha+1)/(alpha-2),(3beta+1)/(beta-2)` c. `(2alpha-1)/(alpha-2),(2beta+1)/(beta-2)` d. none of these

A

`(2alpha + 1)/(alpha - 3), (2beta + 1)/(beta - 3)`

B

`(3alpha + 1)/(alpha - 2), (2beta + 1)/(beta - 2)`

C

`(2alpha - 1)/(alpha - 2), (2beta + 1)/(beta - 2)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
2
`a((2x + 1)^(2))/((x - 3)^(2)) + b((2x + 1))/((x - 3)) + c = 0`
`rArr (2x + 1)/(x - 3) = alpha` or `(2x + 1)/(x - 3) = beta`
or `2x + 1 = alphax - 3alpha`
or `x(alpha - 2) = 1 + 3alpha`
or `x = (1 + 3alpha)/(alpha - 2), (1 + 3beta)/(beta - 2)`
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