CAIE P1 2019 November — Question 6

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2019
SessionNovember
TopicInequalities

6 A line has equation \(y = 3 k x - 2 k\) and a curve has equation \(y = x ^ { 2 } - k x + 2\), where \(k\) is a constant.
  1. Find the set of values of \(k\) for which the line and curve meet at two distinct points.
  2. For each of two particular values of \(k\), the line is a tangent to the curve. Show that these two tangents meet on the \(x\)-axis.