Algebra 02

Algebra Level 4

$\dfrac12 (a + b\alpha + c\alpha^2 + d\alpha^3 ) + \dfrac12 (a + b\beta + c\beta^2 + d\beta^3)$

If $$\alpha$$ and $$\beta$$ are roots to the equation $$6x^2-6x+1 = 0$$, and the value of the expression above can be expressed as $$\dfrac ap + \dfrac bq + \dfrac cr + \dfrac ds$$ for integers $$p,q,r$$ and $$s$$, find the value of $$\dfrac{ r\cdot s}{p \cdot q}$$.

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