| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 1 (Further Pure Core 1) |
| Year | 2021 |
| Session | June |
| Marks | 4 |
| Topic | Complex Numbers Arithmetic |
| Type | Given one complex root of cubic or quartic, find all roots |
| Difficulty | Standard +0.3 This is a standard Further Maths question requiring knowledge that complex roots come in conjugate pairs for real polynomials. Students must identify 2-5i as the second root, expand (x-(2+5i))(x-(2-5i)) to get a quadratic factor, then divide to find the real root. While it requires multiple steps, it follows a well-practiced procedure with no novel insight needed. |
| Spec | 4.02g Conjugate pairs: real coefficient polynomials |
2 In this question you must show detailed reasoning.
You are given that $x = 2 + 5 \mathrm { i }$ is a root of the equation $x ^ { 3 } - 2 x ^ { 2 } + 21 x + 58 = 0$.\\
Solve the equation.
\hfill \mbox{\textit{OCR Further Pure Core 1 2021 Q2 [4]}}