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If alpha and beta are the zeros of the q...

If `alpha` and `beta` are the zeros of the quadratic polynomial `f(x) = x^2 + x -2` , find the value of `1 / alpha - 1 / beta`

A

` -2/3`

B

` -3/2`

C

` (3)/2`

D

` (2)/3`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `ax+by+c=0` be a equation
`alpha+beta = (-b/a)= - 1 and alpha beta = (c/a)= - 2.`
`(beta+alpha)^(2) - (beta-alpha)^(2) = 4 alpha beta`
` rArr (beta-alpha)^(2) = (alpha+beta)^(2) - 4 alpha beta=(-1)^(2) - 4 xx (-2) = 9`
` rArr beta - alpha = 3.`
` :. (1/alpha-1/beta) = ((beta-alpha))/(alpha beta) = 3/(-2) = (-3)/2.`
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