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Algebraic Methods

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Question 82

f(x)=x3−3x+2f(x) = x^3 - 3x + 2f(x)=x3−3x+2

a.

Use the factor theorem to show that (x−1)(x - 1)(x−1) is a factor of f(x)f(x)f(x).

[2]
b.

Hence, show that f(x)=0f(x) = 0f(x)=0 only has two distinct real roots

[4]
c.

Sketch the graph of y=f(x)y = f(x)y=f(x)

[3]
d.

Deduce, giving a reason for your answer, the number of real roots of the equation:

x3−3x+1=0 x^3 - 3x + 1 = 0 x3−3x+1=0
[2]
e.

Given that k k\,k is a constant and the curve with equation y=f(x+k)y = f(x + k)y=f(x+k) passes through the origin, find the two possible values of kkk

[3]
Markscheme

Algebraic Methods Questions

  1. A Level
  2. /Maths
  3. /Algebraic Methods

257 exam-style questions on Edexcel A Level Maths Algebraic Methods, covering 7.1 Algebraic Fractions, 7.2 Dividing Polynomials, 7.3 The Factor Theorem, 7.4 Mathematical Proof, and 7.5 Methods of Proof. Each one has a worked solution and a mark scheme showing where the marks go.

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