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Edexcel A Level Further Maths

Topic questions Pure mathematics Polynomials

Polynomials

8 questions · 68 marks · about 1.5 hours

Polynomials questions

Edexcel 9FM0 Polynomials 8 questions

Paper 1: Core Pure Mathematics 1 June 2024, Question 1 9 marks

f(z) = z4 maths symbol 6z3 maths symbol az2 maths symbol bz maths symbol 145

where a and b are real constants.

Given that 2 + 5i is a root of the equation f(z) = 0

(a)

determine the other roots of the equation f(z) = 0

[7]
Reveal mark scheme Mark scheme for question 1(a)
(b)

Show all the roots of f(z) = 0 on a single Argand diagram.

[2]
Reveal mark scheme Mark scheme for question 1(b)

Paper 1: Core Pure Mathematics 1 June 2024, Question 1 9 marks

f(z) = z4 maths symbol 6z3 maths symbol az2 maths symbol bz maths symbol 145

where a and b are real constants.

Given that 2 + 5i is a root of the equation f(z) = 0

(a)

determine the other roots of the equation f(z) = 0

[7]
Reveal mark scheme Mark scheme for question 1(a)
(b)

Show all the roots of f(z) = 0 on a single Argand diagram.

[2]
Reveal mark scheme Mark scheme for question 1(b)

Paper 1: Core Pure Mathematics 1 June 2022, Question 1 6 marks

f(z) = z3 + az + 52 where a is a real constant

Given that 2 – 3i is a root of the equation f(z) = 0

(a)

write down the other complex root.

[1]
Reveal mark scheme Mark scheme for question 1(a)
(b)

Hence

(b)(i)

solve completely f(z) = 0

Reveal mark scheme Mark scheme for question 1(b)(i)
(b)(ii)

determine the value of a

[4]
Reveal mark scheme Mark scheme for question 1(b)(ii)
(c)

Show all the roots of the equation f(z) = 0 on a single Argand diagram.

[1]
Reveal mark scheme Mark scheme for question 1(c)

Paper 1: Core Pure Mathematics 1 June 2022, Question 1 6 marks

f(z) = z3 + az + 52 where a is a real constant

Given that 2 – 3i is a root of the equation f(z) = 0

(a)

write down the other complex root.

[1]
Reveal mark scheme Mark scheme for question 1(a)
(b)

Hence

(b)(i)

solve completely f(z) = 0

Reveal mark scheme Mark scheme for question 1(b)(i)
(b)(ii)

determine the value of a

[4]
Reveal mark scheme Mark scheme for question 1(b)(ii)
(c)

Show all the roots of the equation f(z) = 0 on a single Argand diagram.

[1]
Reveal mark scheme Mark scheme for question 1(c)

Paper 1: Core Pure Mathematics 1 October 2020, Question 1 10 marks

f (z) = 3z3+pz2+ 57z+q

where p and q are real constants.

Question 1, shown as an image
(a)

show all the roots of f(z) = 0 on a single Argand diagram,

[7]
Reveal mark scheme Mark scheme for question 1(a)
(b)

find the value of p and the value of q.

[3]
Reveal mark scheme Mark scheme for question 1(b)

Paper 1: Core Pure Mathematics 1 November 2020, Question 1 10 marks

f (z) = 3z3+pz2+ 57z+q

where p and q are real constants.

Question 1, shown as an image
(a)

show all the roots of f(z) = 0 on a single Argand diagram,

[7]
Reveal mark scheme Mark scheme for question 1(a)
(b)

find the value of p and the value of q.

[3]
Reveal mark scheme Mark scheme for question 1(b)

Paper 1: Core Pure Mathematics 1 June 2019, Question 1 9 marks

Question 1, shown as an image

where a, b, c and d are real constants.

Given that í1 + 2i and 3 í i are two roots of the equation f (௘zmaths symbol

(a)

=show all the roots of f (௘z௘) = 0 on a single Argand diagram,

[4]
Reveal mark scheme Mark scheme for question 1(a)
(b)

find the values of a, b, c and d.

[5]
Reveal mark scheme Mark scheme for question 1(b)

Paper 1: Core Pure Mathematics 1 June 2019, Question 1 9 marks

where a, b, c and d are real constants.

Given that −1 + 2i and 3 − i are two roots of the equation f (z) = 0

(a)

show all the roots of f (z) = 0 on a single Argand diagram,

[4]
Reveal mark scheme Mark scheme for question 1(a)
(b)

find the values of a, b, c and d.

[5]
Reveal mark scheme Mark scheme for question 1(b)

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