Lesson 6 complex roots of a polynomial equation
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The document discusses complex roots of polynomial equations. It notes that any polynomial with complex roots will have roots that come in conjugate pairs. It asks questions about the relationship between the coefficients of a polynomial and the sum and product of its roots. Specifically, it asks the reader to find the values of a and b for a quartic polynomial given that two of its roots are 3i and 1-2i.
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Lesson 6 complex roots of a polynomial equation
- 2. 2 Sum and Product of Roots What is the relationship of the coefficients of a polynomial and sum of the roots? What is the relationship of the coefficients of a polynomial and the product of the roots? A quartic equation 𝑥! + 𝑎𝑥! + 14𝑥! − 18𝑥 + 𝑏 = 0 has real coefficients and the two of its roots are 3i and 1-2i. Find the values a and b.