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 $10p + q$ ?