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Find the harmonic mean of the roots of t...

Find the harmonic mean of the roots of the equation `(5+sqrt2)x^2-(4+sqrt5)x+(8+2sqrt5)=0`

A

2

B

4

C

6

D

8

Text Solution

Verified by Experts

The correct Answer is:
B
Let `alpha, beta` be the roots of given quadratic equation. Then,
`alpha + beta = (4 + sqrt5)/(5 + sqrt2) and alpha beta = (8 + 2 sqrt5)/(5 + sqrt2)`
Let H be the harmonic mean between `alpha and beta`, then
`H = (2 alpha beta)/(alpha + beta) = (16 + 4 sqrt5)/(4 + sqrt5) = 4`
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