FP1 January 2009 Q1
1. \[\mathrm{f}(x) = 2x^3 - 8x^2 + 7x - 3\]
Given that \(x = 3\) is a solution of the equation \(\mathrm{f}(x) = 0\), solve \(\mathrm{f}(x) = 0\) completely. (5)
| Scheme | Marks |
|---|---|
| \(x - 3\) is a factor | B1 |
| \(\mathrm{f}(x) = (x - 3)(2x^2 - 2x + 1)\) | M1 A1 |
| Attempt to solve quadratic i.e. \(x = \dfrac{2 \pm \sqrt{4 - 8}}{4}\) | M1 |
| \(x = \dfrac{1 \pm \mathrm{i}}{2}\) | A1 |
| [5] |
Notes
First and last terms in second bracket required for first M1
Use of correct quadratic formula for their equation for second M1