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Question 6. Prove by using elementary argument that any polynomial with real coefficients of degree 5 can be represented as a product of linear terms (z - a), where a is a real (constant) number and quadratic terms (22- bz + c), where b, c are also real constants. [Hint: you may assume that roots of polynomials with real coefficients are either real or come in conjugate pairs, i.e. if p(x + iy) = 0, then p(x — iy) = 0.

Question 6. Prove by using elementary argument that any polynomial with real coefficients of degree 5 can be represented as a product of linear terms (z - a), where a is a real (constant) number and quadratic terms (22- bz + c), where b, c are also real constants. [Hint: you may assume that roots of polynomials with real coefficients are either real or come in conjugate pairs, i.e. if p(x + iy) = 0, then p(x — iy) = 0.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 6. Prove by using elementary argument that any polynomial with real coefficients of degree can be represented as a product of linear terms (z − a), where a is a real (constant) number and quadratic terms (z² − bz + c), where b, c are also real constants. [Hint: you may assume that roots of polynomials with real coefficients are either real or come in conjugate pairs, i.e. if p(x + y) = 0, then p(x − iy) = 0.
Transcribed Image Text:Question 6. Prove by using elementary argument that any polynomial with real coefficients of degree can be represented as a product of linear terms (z − a), where a is a real (constant) number and quadratic terms (z² − bz + c), where b, c are also real constants. [Hint: you may assume that roots of polynomials with real coefficients are either real or come in conjugate pairs, i.e. if p(x + y) = 0, then p(x − iy) = 0.
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