| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2015 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Factor & Remainder Theorem |
| Type | Polynomial identity or expansion |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths question requiring algebraic expansion to find coefficients, then solving a quadratic (which happens to have complex roots). The factorization is given, making part (a) routine coefficient matching, and part (b) is standard quadratic formula application. Below average difficulty even for Further Maths F1. |
| Spec | 4.02g Conjugate pairs: real coefficient polynomials4.02i Quadratic equations: with complex roots |
\begin{enumerate}
\item Given that
\end{enumerate}
$$2 z ^ { 3 } - 5 z ^ { 2 } + 7 z - 6 \equiv ( 2 z - 3 ) \left( z ^ { 2 } + a z + b \right)$$
where $a$ and $b$ are real constants,\\
(a) find the value of $a$ and the value of $b$.\\
(b) Given that $z$ is a complex number, find the three exact roots of the equation
$$2 z ^ { 3 } - 5 z ^ { 2 } + 7 z - 6 = 0$$
\hfill \mbox{\textit{Edexcel F1 2015 Q1 [5]}}