Answer the following questions about quadratic polynomials and their zeros.
MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions
Problem
Answer the following questions about quadratic polynomials and their zeros.
(i) Define a monic quadratic polynomial and give one example.
(ii) Explain, with reasons, why two monic quadratic polynomials that share the same pair of zeros must be identical.
(iii) The sum of two real numbers α and β is 5 and their product is 6. Write two different quadratic polynomials that have α and β as their zeros, and state which of them is monic. Justify your answer.