OCR MEI FP1 2013 June — Question 2 6 marks

Exam BoardOCR MEI
ModuleFP1 (Further Pure Mathematics 1)
Year2013
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicRoots of polynomials
TypeFactor theorem and finding roots
DifficultyModerate -0.5 This is a straightforward application of the factor theorem requiring polynomial division and solving a quadratic. Given one root explicitly, students factor out (2z-3), perform division, then solve the resulting quadratic—all standard techniques with no conceptual challenges beyond routine algebraic manipulation.
Spec1.02f Solve quadratic equations: including in a function of unknown1.02j Manipulate polynomials: expanding, factorising, division, factor theorem

2 You are given that \(z = \frac { 3 } { 2 }\) is a root of the cubic equation \(2 z ^ { 3 } + 9 z ^ { 2 } + 2 z - 30 = 0\). Find the other two roots.

2 You are given that $z = \frac { 3 } { 2 }$ is a root of the cubic equation $2 z ^ { 3 } + 9 z ^ { 2 } + 2 z - 30 = 0$. Find the other two roots.

\hfill \mbox{\textit{OCR MEI FP1 2013 Q2 [6]}}