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If alpha and beta are the roots of the e...

If `alpha and beta` are the roots of the equation `x^(2) +6x + 1 = 0 ," then what is "|alpha - beta|` equal to?

A

6

B

`3sqrt(3)`

C

`4sqrt(2)`

D

12

Text Solution

Verified by Experts

The correct Answer is:
C
`alpha and beta` are the rrots of the equation `x^(2) + 6x + 1 = 0 `
` rArr alpha + beta = -6 and alphabeta = 1 `
Now, `(alpha -beta)^(2) = (alpha + beta)^(2)- 4alphabeta`
`= (-6)^(2) - 4 = 36 - 4 =32`
` rArr |alpha - beta|= sqrt (32)=4 sqrt(2)`
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