OCR FP1 Specimen — Question 2

Exam BoardOCR
ModuleFP1 (Further Pure Mathematics 1)
SessionSpecimen
TopicRoots of polynomials

2 The cubic equation \(x ^ { 3 } - 6 x ^ { 2 } + k x + 10 = 0\) has roots \(p - q , p\) and \(p + q\), where \(q\) is positive.
  1. By considering the sum of the roots, find \(p\).
  2. Hence, by considering the product of the roots, find \(q\).
  3. Find the value of \(k\).