This discussion is now closed.
Check out other Related discussions
- Econ+Maths joint honours, or straight Econ?
- Edexcel A-level Further Mathematics Paper 3A - 18th June 2025 [Exam Chat]
- Edexcel A-level further mathematics grade boundaries 2024
- Is it possible to get into LSE BSc finance without FM
- What's the hardest A-level maths topic?
- Edexcel A-Level FP1 and FP2
- Help pls fp1
- Whats Decision Maths all about?
- Isaac Physics question - standing waves
- Maths vs Maths and Stats vs Maths and Phys degrees
- Do I have a chance of getting into Cambridge for NatSci with A*A*AA?
- maths degree - help - about maths degree
- Books to read to prepare for maths at university
- AS level subjects
- How hard is it to get A* in Further Maths A level?
- GYG of a homeschooled American girl :)
- A Level Further Maths Options
- How to get into cambridge for CS
- A question about admission to a math master's program with an unrelated bachleor's
- What is university maths actually like?
FP1 Algebra
Can anyone help me with this question:
The equation Z^3-KZ^2-4z-12=0 has roots α, β and γ.
(i) Write down the values of αβ + βγ + γα and αβγ, and express k in terms of α, β and γ.
(ii) For the case where γ = –α, solve the equation and find the value of k.
(iii) For the case k = 5, find a cubic equation with roots 2 – α, 2 – β, 2 – γ.
The equation Z^3-KZ^2-4z-12=0 has roots α, β and γ.
(i) Write down the values of αβ + βγ + γα and αβγ, and express k in terms of α, β and γ.
(ii) For the case where γ = –α, solve the equation and find the value of k.
(iii) For the case k = 5, find a cubic equation with roots 2 – α, 2 – β, 2 – γ.
Reply 1
Well. There's some theorem (fundamental theorem of algebra is it? I don't know.) that's like...any polynomial can be factorised (uniquely too) into as many brackets as it has roots.
Anyway. Write
z³-kz²-4z-12
as
(z-α
(z-β(z-γ
and multiply out. That should start you off. :x
Anyway. Write
z³-kz²-4z-12
as
(z-α
(z-β(z-γand multiply out. That should start you off. :x
Reply 2
For an equation ax^3 + bx^2 + cx + d = 0, with roots α, β, γ, you should know that:
α+β+γ = -b/a
αβ+αγ+βγ = +c/a
αβγ = -d/a.
α+β+γ = -b/a
αβ+αγ+βγ = +c/a
αβγ = -d/a.
Related discussions
- Econ+Maths joint honours, or straight Econ?
- Edexcel A-level Further Mathematics Paper 3A - 18th June 2025 [Exam Chat]
- Edexcel A-level further mathematics grade boundaries 2024
- Is it possible to get into LSE BSc finance without FM
- What's the hardest A-level maths topic?
- Edexcel A-Level FP1 and FP2
- Help pls fp1
- Whats Decision Maths all about?
- Isaac Physics question - standing waves
- Maths vs Maths and Stats vs Maths and Phys degrees
- Do I have a chance of getting into Cambridge for NatSci with A*A*AA?
- maths degree - help - about maths degree
- Books to read to prepare for maths at university
- AS level subjects
- How hard is it to get A* in Further Maths A level?
- GYG of a homeschooled American girl :)
- A Level Further Maths Options
- How to get into cambridge for CS
- A question about admission to a math master's program with an unrelated bachleor's
- What is university maths actually like?
Latest
Trending
Last reply 7 hours ago
Edexcel AS Level Maths May 15th 2025 Pure Paper 1 + Unofficial Mark SchemeMaths Study Help
62
159
Last reply 1 month ago
Further mechanics 2 options overlapping with physics rather than stats?
