Complex roots, sum and product

1. 1
Complex Roots of a Polynomial Equation
What is the Fundamental Theorem of Algebra?
If a quadratic has no real roots the imaginary roots are:____________________
Given that z = 2+i is a root of the equation z3-3z2+z+5 = 0 find the other two
roots.
What do you notice about the other two roots?
If any polynomial has complex roots then these will always be _______________
Possible combinations of roots:
Polynomial
degree
2 Two real roots Two imaginary
roots
3
4
5

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.