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The roots of the equation x^(4)-2x^(2)+4...

The roots of the equation `x^(4)-2x^(2)+4=0` are the vertices of `a` :

A

square inscribed in a circle of radius `2`

B

rectangle inscribed in a circle of radius `2`

C

square inscribed in a circle of radius `sqrt(2)`

D

rectangle inscribed in a circle of radius `sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `x^(4)-2x^(2)+4=0`
`impliesx^(2)=1+-sqrt(3)i`
`=2e^(+-(pi)/(3))`
`implies x=+-sqrt(2)e^(+-i(pi)/(6))`
These points lie on a circle of radius `sqrt(2)`, as the diagonals intersect at an angle `pi//3`,
`:.` These are the vertices of an inscribed rectangle.
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