# Meticulous design

Algebra Level 4

Let $$w$$ denote a non-real complex number where $$w^7 = 1$$. Define $$a = w+w^2+w^4$$ and $$b = w^3 + w^5 + w^6$$.

If $$a$$ and $$b$$ are roots of the equation $$x^2+px+q=0$$ for constants $$p$$ and $$q$$, what is the value of $$10p + q$$?

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