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1 Unit 1: Pure Mathematics A

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Question 6

f(x)=2x3−5x2−4x+12f(x) = 2x^3 - 5x^2 - 4x + 12f(x)=2x3−5x2−4x+12

a.

Use the factor theorem to show that (x−2)(x - 2)(x−2) 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:

2x3−5x2−4x+10=0 2x^3 - 5x^2 - 4x + 10 = 0 2x3−5x2−4x+10=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

1 Unit 1: Pure Mathematics A Questions

  1. A Level
  2. /Maths
  3. /1 Unit 1: Pure Mathematics A

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