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−12y=2x-12y=2x−12.
Show that 9p2−8p+1<09p^2-8p+1<09p2−8p+1<0.
Find the set of possible values for ppp.
37 exam-style questions on Edexcel AS 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.