# Dare to find my roots!

Algebra Level 5

$x^5+5\lambda x^4-x^3+(\lambda \alpha -4)x^2-(8\lambda+3)x+(\lambda \alpha -2)=0 \\ \lambda,\alpha \in \mathbb{R}$ If the value of $$\alpha$$ for which the above equation has exactly one root independent of $$\lambda$$ is in the form $$-\dfrac{a}{b}$$ where $$a$$ and $$b$$ are coprime positive integers, find $$a+b$$.

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