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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de azalea