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Construct the quadratic equation with following given roots `(7+sqrt(5))/7 and (7-sqrt(5))/7`

Text Solution

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Given roots are `(7+sqrt5)/7` and `(7-sqrt5)/7`.
Sum of roots `= 1/7(7+sqrt5+7-sqrt5) = 14/7 = 2`
Product of roots ` = (7+sqrt5)/7**(7-sqrt5)/7 = 44/49`
Now, we can construct a quadratic equation as,
`=>x^2 - `(sum of roots)`x+` product of roots` = 0`
`=>x^2-2x+44/49 = 0`
`=>49x^2-98x+44 = 0`, which is the required equation.
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