Higher June 2023 Paper 2 Q17
17. The diagram shows the graphs of \(y = x^2 + \dfrac{1}{x}\) and \(y = 2x + 1\) for values of \(x\) between \(-2\) and 3.
(a) Show that where the line and curve intersect, \(x\) satisfies the equation
\(x^3 - 2x^2 - x + 1 = 0\). [3]
\(x^3 - 2x^2 - x + 1 = 0\). [3]
(b) Write down the solutions to the equation \(x^3 - 2x^2 - x + 1 = 0\).
Give your answers correct to 1 decimal place. [2]
Give your answers correct to 1 decimal place. [2]
| Scheme | Marks | Comments |
|---|---|---|
| \(x^2 + \dfrac{1}{x} = 2x + 1\) | M1 | |
| \(x^3 + 1 = 2x^2 + x\) | M1 | |
| Correct completion to \(x^3 - 2x^2 - x + 1 = 0\) | A1 |
| Scheme | Marks | Comments |
|---|---|---|
| (\(x\) =) \(-0.8\), 0.5 or 0.6, 2.2 or 2.3 | B2 | B1 for any two correct or for answers given as coordinates or for 3 correct values not rounded to 1dp (\(-0.8019\ldots\), 0.5549…, 2.246…) |
| (5) |