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Date May 2018 Marks available 5 Reference code 18M.2.AHL.TZ2.H_2
Level Additional Higher Level Paper Paper 2 Time zone Time zone 2
Command term Find Question number H_2 Adapted from N/A

Question

The polynomial x4+px3+qx2+rx+6 is exactly divisible by each of (x1)(x2) and (x3).

Find the values of pq and r.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

METHOD 1

substitute each of x = 1,2 and 3 into the quartic and equate to zero      (M1)

p+q+r=7

4p+2q+r=11 or equivalent        (A2)

9p+3q+r=29

Note: Award A2 for all three equations correct, A1 for two correct.

attempting to solve the system of equations      (M1)

p = −7, q = 17, r = −17     A1

Note: Only award M1 when some numerical values are found when solving algebraically or using GDC.

 

METHOD 2

attempt to find fourth factor      (M1)

(x1)     A1

attempt to expand (x1)2(x2)(x3)     M1

x47x3+17x217x+6 (p = −7, q = 17, r = −17)     A2

Note: Award A2 for all three values correct, A1 for two correct.

Note: Accept long / synthetic division.

[5 marks]

Examiners report

[N/A]

Syllabus sections

Topic 2—Functions » AHL 2.12—Factor and remainder theorems, sum and product of roots
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Topic 2—Functions

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