# 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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