Edexcel FP1 — Question 42 6 marks

Exam BoardEdexcel
ModuleFP1 (Further Pure Mathematics 1)
Marks6
PaperDownload PDF ↗
TopicFactor & Remainder Theorem
TypeGiven factor, find all roots
DifficultyStandard +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.
Spec4.02g 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]

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]}}