| Date | May 2014 | Marks available | 6 | Reference code | 14M.1.hl.TZ1.4 |
| Level | HL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 4 | Adapted from | N/A |
Question
The equation \(5{x^3} + 48{x^2} + 100x + 2 = a\) has roots \({r_1}\), \({r_2}\) and \({r_3}\).
Given that \({r_1} + {r_2} + {r_3} + {r_1}{r_2}{r_3} = 0\), find the value of a.
Markscheme
\({r_1} + {r_2} + {r_3} = \frac{{ - 48}}{5}\) (M1)(A1)
\({r_1}{r_2}{r_3} = \frac{{a - 2}}{5}\) (M1)(A1)
\(\frac{{ - 48}}{5} + \frac{{a - 2}}{5} = 0\) M1
\(a = 50\) A1
Note: Award M1A0M1A0M1A1 if answer of 50 is found using \(\frac{{48}}{5}\) and \(\frac{{2 - a}}{5}\).
[6 marks]
Examiners report
[N/A]
