Writing the equation of a polynomial given a complex root

The video tutorial explains how to work with complex zeros and their conjugates in polynomials. It begins by introducing the concept of complex zeros and the importance of considering their conjugates. The tutorial then demonstrates how to set these zeros to X values and apply the zero product property to find polynomials. The difference of two squares method is explained as a way to simplify multiplication. The session concludes with forming and simplifying polynomials, emphasizing the process of working backwards from given zeros.

What must be considered when given a complex zero in a polynomial?

• The real part of the zero

• The complex conjugate of the zero

• The imaginary part of the zero

• The zero itself

What property is used to find the polynomial from given zeros?

• Commutative Property

• Zero Product Property

• Associative Property

• Distributive Property

What is the result of multiplying (X - 3i) and (X + 3i)?

• X^2 - 9

• X^2 + 9

• X^2 - 6i

• X^2 + 6i

Which method is used to simplify the expression (X - 3i)(X + 3i)?

• Completing the square

• Difference of squares

• Quadratic formula

• Synthetic division

What happens to the terms -3ix and 3ix in the expression (X - 3i)(X + 3i)?

• They add up to zero

• They multiply to form a new term

• They remain unchanged

• They form a complex number