Roots with special relationships

A question is this type if and only if it states that roots satisfy a specific relationship (like α = β, or roots in arithmetic/geometric progression, or α = 1/β) and asks to find coefficients or root values.

26 questions · Standard +0.8

4.05a Roots and coefficients: symmetric functions
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OCR MEI Further Pure Core AS Specimen Q5
7 marks Challenging +1.2
The cubic equation \(x^3 - 4x^2 + px + q = 0\) has roots \(\alpha\), \(\frac{2}{\alpha}\) and \(\alpha + \frac{2}{\alpha}\). Find
  • the values of the roots of the equation,
  • the value of \(p\).
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