Worksheet: Linear Factorization and Conjugate Root Theorems
In this worksheet, we will practice writing a polynomial function given its zeros using linear factorization and conjugate root theorems.
Q1:
Write a polynomial function of the least degree with real coefficients in standard form given that it has , and as zeros.
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Q2:
Write a polynomial function of least degree with real coefficients in standard form given that it has and (multiplicity 2) as zeros.
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Q3:
Write a polynomial function of the least degree with real coefficients in standard form given that it has , and as zeros.
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Q5:
Consider .
Write as the product of linear and irreducible quadratic factors.
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List all zeros of .
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Q7:
Consider .
Write as the product of linear and irreducible quadratic factors.
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Write as the product of linear factors.
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List all zeros of .
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Q9:
What is the least possible degree of a polynomial function with rational coefficients, given that it has (multiplicity 2), , and (multiplicity 3) as zeros?
Q10:
What is the least possible degree of a polynomial function with rational coefficients, given that it has , , and as zeros?