# Algebra + Geometry

Algebra Level 4

$12x^{4}-56x^{3}+89x^{2}-56x+12$

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 $$a+b$$.

×