| Exam Board | CAIE |
|---|---|
| Module | Further Paper 1 (Further Paper 1) |
| Year | 2022 |
| Session | June |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Roots of polynomials |
4 The cubic equation $2 x ^ { 3 } + 5 x ^ { 2 } - 6 = 0$ has roots $\alpha , \beta , \gamma$.\\
(a) Find a cubic equation whose roots are $\frac { 1 } { \alpha ^ { 3 } } , \frac { 1 } { \beta ^ { 3 } } , \frac { 1 } { \gamma ^ { 3 } }$.\\
(b) Find the value of $\frac { 1 } { \alpha ^ { 6 } } + \frac { 1 } { \beta ^ { 6 } } + \frac { 1 } { \gamma ^ { 6 } }$.\\
(c) Find also the value of $\frac { 1 } { \alpha ^ { 9 } } + \frac { 1 } { \beta ^ { 9 } } + \frac { 1 } { \gamma ^ { 9 } }$.\\
\hfill \mbox{\textit{CAIE Further Paper 1 2022 Q4}}