Consider the cubic equation x^(3)-(1+c...

Consider the cubic equation
`x^(3)-(1+cos theta+sin theta)x^(2)+(cos theta sin theta +cos theta + sin theta)x - sin theta cos theta =0`. When roots are `x_(1),x_(2)` and `x_(3)`.
The value of `x_(1)^(2)+x_(2)^(2)+x_(3)^(2)` equals

`2cos theta`

`sin theta(sin theta+cos theta)`

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Consider the cubic equation x^(3)-(1+cos theta+sin theta)x^(2)+(cos theta sin theta +cos theta + sin theta)x - sin theta cos theta =0 . When roots are x_(1),x_(2) and x_(3) . Number of values of theta in [0,2pi] for which at least two roots are equal

`sqrt(2)`

`a^(2)+b^(2) = x^(2)+y^(2) `

`x^(2)//a^2 + y^(2)//b^(2) =2 `

xy=ab

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