CAIE Further Paper 1 2022 June — Question 4

Exam BoardCAIE
ModuleFurther Paper 1 (Further Paper 1)
Year2022
SessionJune
TopicRoots of polynomials

4 The cubic equation \(2 x ^ { 3 } + 5 x ^ { 2 } - 6 = 0\) has roots \(\alpha , \beta , \gamma\).
  1. Find a cubic equation whose roots are \(\frac { 1 } { \alpha ^ { 3 } } , \frac { 1 } { \beta ^ { 3 } } , \frac { 1 } { \gamma ^ { 3 } }\).
  2. Find the value of \(\frac { 1 } { \alpha ^ { 6 } } + \frac { 1 } { \beta ^ { 6 } } + \frac { 1 } { \gamma ^ { 6 } }\).
  3. Find also the value of \(\frac { 1 } { \alpha ^ { 9 } } + \frac { 1 } { \beta ^ { 9 } } + \frac { 1 } { \gamma ^ { 9 } }\).