OCR Further Pure Core AS 2022 June — Question 3

Exam BoardOCR
ModuleFurther Pure Core AS (Further Pure Core AS)
Year2022
SessionJune
TopicRoots of polynomials

3 In this question you must show detailed reasoning. The roots of the equation \(5 x ^ { 3 } - 3 x ^ { 2 } - 2 x + 9 = 0\) are \(\alpha , \beta\) and \(\gamma\).
Find a cubic equation with integer coefficients whose roots are \(\alpha \beta , \beta \gamma\) and \(\gamma \alpha\).