JEE maths#16

Geometry Level 4

If \(\cos^{4} ( \theta) + \alpha\) and \(\sin^{4} ( \theta ) +\alpha \) are the roots of the equation \( x^{2} + b(2x+1) = 0\), and \( \cos^{2} ( \theta ) + \beta\) and \(\sin^{2} ( \theta ) + \beta \) are the roots of the equation \( x^{2} + 4x + 2 = 0 \), then find the value of positive integer \(b \).

Note :- \( \theta \) can be a non- real number as well \[\]


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