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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