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 AQA A Level Maths 1.5 B: Algebra and functions with exam-style questions for A Level Maths. 358 questions covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 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.
