CAIE Further Paper 1 2020 June — Question 1

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

1 The cubic equation \(7 x ^ { 3 } + 3 x ^ { 2 } + 5 x + 1 = 0\) has roots \(\alpha , \beta , \gamma\).
  1. Find a cubic equation whose roots are \(\alpha ^ { - 1 } , \beta ^ { - 1 } , \gamma ^ { - 1 }\).
  2. Find the value of \(\alpha ^ { - 2 } + \beta ^ { - 2 } + \gamma ^ { - 2 }\).
  3. Find the value of \(\alpha ^ { - 3 } + \beta ^ { - 3 } + \gamma ^ { - 3 }\).