| Exam Board | Edexcel |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Given factor, find all roots |
| Difficulty | Standard +0.3 This is a straightforward application of the factor theorem followed by quadratic formula with complex roots. Given one root, students factor out (2x+1), perform polynomial division to get a quadratic, then solve using standard methods. While it involves complex numbers (FP1 content), the procedure is mechanical with no problem-solving insight required, making it slightly easier than average. |
| Spec | 4.02g Conjugate pairs: real coefficient polynomials4.02i Quadratic equations: with complex roots |
Given that $x = -\frac{1}{2}$ is the real solution of the equation
$$2x^3 - 11x^2 + 14x + 10 = 0,$$
find the two complex solutions of this equation.
[6]
\hfill \mbox{\textit{Edexcel FP1 Q42 [6]}}