The curve with equation y=px2−4px−5py=px^2-4px-5py=px2−4px−5p, where p p\,p is a constant, does not intersect the line with equation y=2x−ky=2x-ky=2x−k, where k>10k>10k>10.
Show that 9p2+(4−k)p+1<09p^2+(4-k)p+1<09p2+(4−k)p+1<0.
Find the set of possible values for p p\,p in terms of kkk.
322 exam-style questions on Edexcel A Level Maths Quadratics, covering 2.1 Solving Quadratics, 2.2 Completing the Square, 2.3 Sketching Quadratic Graphs, 2.4 The Discriminant, and 2.5 Modelling with Quadratics. Each one has a worked solution and a mark scheme showing where the marks go.