AS June 2025 Paper 1 Q5
5 The quartic equation
\[3x^4 + x^2 - 5x - 11 = 0\]has roots \(\alpha, \beta, \gamma\) and \(\delta\)
(a) Write down the value of \(\alpha\beta\gamma\delta\) [1 mark]
(b) Write down the value of \(\alpha\beta\gamma + \alpha\beta\delta + \alpha\gamma\delta + \beta\gamma\delta\) [1 mark]
| Scheme | Marks | AO |
|---|---|---|
| Obtains \(-\dfrac{11}{3}\) | B1 | 1.1b |
| (1) |
Typical solution
\[\alpha\beta\gamma\delta = -\frac{11}{3}\]| Scheme | Marks | AO |
|---|---|---|
| Obtains \(\dfrac{5}{3}\) | B1 | 1.1b |
| (1) | ||
| (2 marks) |