Meticulous design

Algebra Level 4

Let ww denote a non-real complex number where w7=1w^7 = 1 . Define a=w+w2+w4a = w+w^2+w^4 and b=w3+w5+w6b = w^3 + w^5 + w^6.

If aa and bb are roots of the equation x2+px+q=0x^2+px+q=0 for constants pp and qq, what is the value of 10p+q10p + q ?

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