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If alpha and beta ar the zeros of the po...

If `alpha` and `beta` ar the zeros of the polynomial `f(x)=x^2-5x+k` such that `alpha-beta=1,` find the value of `k`

A

6

B

5

C

4

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
`(alpha + beta) = 5 and alpha beta = k," Also, " alpha - beta = 1 ` (given).
`:. (alpha+beta)^(2) - (alpha-beta)^(2) = 4alpha beta rArr 5^(2) - 1^(2) = 4 alpha beta`
` :. 4alpha beta = (25 -1) = 24 rArr alpha beta = 6.`
Hence, k = 6.
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