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Question 32

The curve $C\,$ has the equation $y=1x+kx∈R,x≠0\displaystyle y = \frac{1}{x} + k \quad x \in \mathbb{R}, x \neq 0$

The line $L\,$ has the equation $y = - 3 x + 2$

Show that the $x$ -coordinate of any point of intersection of $L\,$ with $C\,$ is given by a solution of the equation

3x^2 + (k - 2)x + 1 = 0

[3]

Hence find the exact values of $k\,$ for which $L\,$ is a tangent of $C$ .

[3]

Markscheme

Quadratics Questions

A Level
Maths
Quadratics

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.

Quadratics

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Quadratics

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Question 32

The curve $C\,$ has the equation $y=1x+kx∈R,x≠0\displaystyle y = \frac{1}{x} + k \quad x \in \mathbb{R}, x \neq 0$

The line $L\,$ has the equation $y = - 3 x + 2$

Show that the $x$ -coordinate of any point of intersection of $L\,$ with $C\,$ is given by a solution of the equation

3x^2 + (k - 2)x + 1 = 0

[3]

Hence find the exact values of $k\,$ for which $L\,$ is a tangent of $C$ .

[3]

Markscheme

Quadratics Questions

A Level
Maths
Quadratics