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The harmonic mean of the roots of the eq...

The harmonic mean of the roots of the equation `(5+sqrt(2))x^2-(4+sqrt(5))x+8+2sqrt(5)=0` is a. `2` b. `4` c. `6` d. `8`

Text Solution

Verified by Experts

The correct Answer is:
4
We have `(5+sqrt(2))x^(2)-(4+sqrt(5))x+8+2sqrt(5)=0`
`:.` Sum of the roots `=(4+sqrt(5))/(5+sqrt(2))`
and product of the roots `=(8+2sqrt(5))/(5+sqrt(2))`
and product of the roots `=(8+2sqrt(5))/(5+sqrt(2))`
`:.` The harmonic mean of the roots
`=(2xx"Product of the roots")/("Sum of the roots")=(2xx(8+2sqrt(5)))/((4+sqrt(5)))=4`
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