Skip to content

Course home

Sign up

Algebraic Methods

EasyMediumHard
1234567
Question 6

f(x)=2x3−ax2+6x+18f(x) = 2x^3 - ax^2 + 6x + 18f(x)=2x3−ax2+6x+18

a.

Given that (x−3)(x - 3)(x−3) is a factor of f(x)f(x)f(x), use the factor theorem to find the value of aaa.

[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:

2x3−10x2+6x+16=0 2x^3 - 10x^2 + 6x + 16 = 0 2x3−10x2+6x+16=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.

Question bank