\(\displaystyle a = \int_0^{1} \arctan (1- x + x^2) \, dx \)

Find the other root of a quadratic polynomial which has one of its roots as \( a \) and has its minimum at \( \ln \sqrt{2} \).

**Details and Clarifications**:

A number \(p\) is said to be a root of a polynomial \(f(x)\) if \(f(p) = 0\).

\(\displaystyle \arctan p \) is the same as \( \tan^{-1} p \).

\(\displaystyle \ln p \) is the same as \( \log_e p \).

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