Edexcel A Level Further Maths
Topic questions Pure mathematics Roots of polynomials
7 questions · 56 marks · about 1 hour
The quartic equation
where A is a real constant, has roots 
, 
, and 
Determine the value of
determine the possible values of A
The roots of the equation
are α, β and γ
Without solving the equation,
write down the value of each of
α + β + γ αβ + αγ + βγ αβγ
Use the answers to part (a) to determine the value of
(α – 1)(β – 1)(γ – 1)
α2 + β2 + γ2
The roots of the equation
are α, β and γ
Without solving the equation,
Use the answers to part (a) to determine the value of
(α – 1)(β – 1)(γ – 1)
α2 + β2 + γ2
The cubic equation
where p and q are real positive constants, has roots α, β and γ
Given that α2 + β2 + γ2 = 16
show that p = 12
determine the value of q
Without solving the cubic equation,
determine the value of (α – 1)(β – 1)(γ – 1)
The cubic equation
where p and q are real positive constants, has roots α, β and γ
Given that α2 + β2 + γ2 = 16
show that p = 12
determine the value of q
Without solving the cubic equation,
determine the value of (α – 1)(β – 1)(γ – 1)
The cubic equation
where a and b are constants, has roots α, β and γ
The cubic equation
where c is a constant, has roots (4α – 1), (4β – 1) and (4γ – 1)
Without solving either cubic equation, determine the value of a, the value of b and the value of c.
The cubic equation
where a and b are constants, has roots α, β and γ
The cubic equation
where c is a constant, has roots (4α – 1), (4β – 1) and (4γ – 1)
Without solving either cubic equation, determine the value of a, the value of b and the value of c.
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