Comprehension
Consider the cubic equation \( x^{3}-(1 \) \( +\cos \theta+\sin \theta) x^{2}+(\co...
Comprehension
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 where \( x_{1}, x_{2}, x_{3} \) are roots.
Greatest possible difference between two of roots if \( \theta \in[0,2 \pi] \) is
(a) \( 2 \sqrt{2} \)
(b) 1
(c) \( \sqrt{2} \)
(d) 2
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