OCR MEI Further Pure Core AS Specimen — Question 8

Exam BoardOCR MEI
ModuleFurther Pure Core AS (Further Pure Core AS)
SessionSpecimen
TopicComplex Numbers Arithmetic
TypeGeometric properties using complex numbers

8 In this question you must show detailed reasoning.
  1. Explain why all cubic equations with real coefficients have at least one real root.
  2. Points representing the three roots of the equation \(z ^ { 3 } + 9 z ^ { 2 } + 27 z + 35 = 0\) are plotted on an Argand diagram. Find the exact area of the triangle which has these three points as its vertices.