CAIE Further Paper 1 2020 Specimen — Question 4

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

4 Th cb c ę tin $$z ^ { 3 } - z ^ { 2 } - z - 5 = 0$$ h s ro \(\mathrm { s } \alpha , \beta\) ad \(\gamma\).
  1. Sth th t th le \(6 \alpha ^ { 3 } + \beta ^ { 3 } + \gamma ^ { 3 }\) is 9
  2. Fid he le \(6 \alpha ^ { 4 } + \beta ^ { 4 } + \gamma ^ { 4 }\).
  3. Fird cb ceq tin \(N\) ith o s \(\alpha + 1 \beta + 1 \mathrm {~d} \gamma + \underset { \text { g } } { \text { vg } } \quad\) as wer in th fo m $$p x ^ { 3 } + q x ^ { 2 } + r x + s = 0$$ we re \(p , q , r\) ad \(s\) are co tan s to \(\mathbf { b } \quad \mathbf { d }\) termin d