The curve C C\,C has the equation y=2x+kx∈R,x≠0\displaystyle y = \frac{2}{x} + k \quad x \in \mathbb{R}, x \neq 0y=x2+kx∈R,x=0
The line L L\,L has the equation y=−3x+2y = -3x + 2y=−3x+2
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
3x2+(k−2)x+2=0 3x^2 + (k - 2)x + 2 = 0 3x2+(k−2)x+2=0Hence find the exact values of k k\,k for which L L\,L is a tangent of CCC.
Practise Edexcel AS Level Maths Quadratics with exam-style questions for AS Level Maths. 25 questions 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, matched to the Edexcel AS Level Maths (8MA0) specification and written in Paper 1 and Paper 2 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.