| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2014 |
| Session | June |
| Marks | 4 |
| Topic | Complex Numbers Arithmetic |
| Type | Quadratic from one complex root |
| Difficulty | Easy -1.2 This is a straightforward application of the conjugate root theorem for quadratics with real coefficients, followed by routine use of Vieta's formulas or expansion. It requires only standard recall and basic arithmetic with complex numbers, making it easier than average with no problem-solving insight needed. |
| Spec | 4.02g Conjugate pairs: real coefficient polynomials4.02i Quadratic equations: with complex roots |
State $3 - \mathrm{i}$ — B1
Attempt a complete method for determining $p$ and $q$ — M1
Obtain $p = -6$ — A1
Obtain $q = 10$ — A1 **[4]**5 A root of the equation $z ^ { 2 } + p z + q = 0$ is $3 + \mathrm { i }$, where $p$ and $q$ are real. Write down the other root of the equation and hence calculate the values of $p$ and $q$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2014 Q5 [4]}}