The curve C C\,C has the equation y=5x+kx∈R,x≠0\displaystyle y = \frac{5}{x} + k \quad x \in \mathbb{R}, x \neq 0y=x5+kx∈R,x=0
The line L L\,L has the equation y=−2x+3y = -2x + 3y=−2x+3
Show that the xxx-coordinate of any point of intersection of L L\,L with C C\,C is given by a solution of the equation
2x2+(k−3)x+5=0 2x^2 + (k - 3)x + 5 = 0 2x2+(k−3)x+5=0Hence find the exact values of k k\,k for which L L\,L is a tangent of CCC.
211 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.