CAIE Further Paper 1 2020 June — Question 2

Exam BoardCAIE
ModuleFurther Paper 1 (Further Paper 1)
Year2020
SessionJune
TopicRoots of polynomials

2 The cubic equation \(6 \mathrm { x } ^ { 3 } + \mathrm { px } ^ { 2 } - 3 \mathrm { x } - 5 = 0\), where \(p\) is a constant, has roots \(\alpha , \beta , \gamma\).
  1. Find a cubic equation whose roots are \(\alpha ^ { 2 } , \beta ^ { 2 } , \gamma ^ { 2 }\).
  2. It is given that \(\alpha ^ { 2 } + \beta ^ { 2 } + \gamma ^ { 2 } = 2 ( \alpha + \beta + \gamma )\).
    1. Find the value of \(p\).
    2. Find the value of \(\alpha ^ { 3 } + \beta ^ { 3 } + \gamma ^ { 3 }\).