Algebra + Geometry

Algebra Level 4


Given that the roots of the polynomial above are \(x_{1},x_{2},x_{3},x_{4}\) in increasing order.

Find the area of the quadrilateral with vertices \[(\lfloor x_{1} \rfloor^{2},\lfloor x_{2} \rfloor^{2}),(\lfloor x_{2} \rfloor^{2},\lfloor x_{3} \rfloor^{2}),(\lfloor x_{3} \rfloor^{2},\lfloor x_{4} \rfloor^{2}),(\lfloor x_{4} \rfloor^{2},\lfloor x_{1} \rfloor^{2}).\]

If your answer comes as \(\dfrac{a}{b}\) where \(a\) and \(b\) are coprime positive integers, submit your answer as \(a+b\).


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