Maths Extension 1 Year 11 - Module 2 - Lesson 6
Sums and Products of Roots, Quadratics
Name
Date
Class
1. Lesson focus
Sums and products of quadratic roots. For ax²+bx+c=0 with roots α,β, α+β=−b/a and αβ=c/a; use these to form expressions without solving when possible.
Success criteria
- Apply the lesson method accurately in a routine example.
- Show each algebraic or domain step and check the result.
- Explain why the method and restrictions fit the question.
2. Worked practice
2. If α,β are roots of x²−7x+10=0, find α²+β².
3. Write a monic quadratic with roots 2 and 3.
3. Challenge
For roots 4 and −1, find α²+β² and form their monic quadratic.
4. Multiple choice
For ax²+bx+c=0, the product of its roots is what?
A. −b/a
B. c/a
C. −c/a
D. b/a
Worked answer key
Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.
1. Find the sum and product of roots of x²−7x+10=0.
Sum=7 and product=10.
2. If α,β are roots of x²−7x+10=0, find α²+β².
(α+β)²−2αβ=7²−20=29.
3. Write a monic quadratic with roots 2 and 3.
Sum 5, product 6: x²−5x+6=0.
Challenge. For roots 4 and −1, find α²+β² and form their monic quadratic.
Sum=3, product=−4; α²+β²=3²−2(−4)=17; polynomial x²−3x−4.
Multiple choice. For ax²+bx+c=0, the product of its roots is what?
Correct answer: B. Vieta's product relation is αβ=c/a; the sum is −b/a.
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