Real roots and variation of the constant term for a cubic polynomial

Calculus Level 4

Let \(P(x)=x^3+x^2+c\) a polynomial where \(c\) is a real number. Then there is a finite interval \(I\) such that, \(P(x)\) has more than one real root if and only if \(c\) is in \(I\). If the length of \(I\) can be represented as a number of the form \(\frac{a}{b},\) where \(a\) and \(b\) are coprimes, then find \(a+b.\)


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