# Inspired by problem 3, IMO 1973

Calculus Level 5

$\large x^4+ a x^3 + x^2 + b x+1=0$Let $$A$$ be the set of points $$(a,b)$$ for which the above equation has no real root. Area of $$A$$ can be expressed as$\frac{p\sqrt{q}}{r}+ s \ \tanh ^{-1} \left( \sqrt{\frac{t}{u}} \right)$Find the value of $$p+q+r+s+t+u$$.

Details and Assumptions:

• $$a$$, $$b$$ are real numbers.
• $$p$$, $$q$$, $$r$$, $$s$$, $$t$$ and $$u$$ are positive integers, $$q$$ is square free and $$\gcd(p, r)=\gcd(t, u)=1$$.
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