Polynomial Functions and Complex Zeros

The video tutorial explains how to find a polynomial function with real coefficients given specific zeros, including complex zeros. It covers the relationship between zeros and polynomial factors, emphasizing that complex zeros appear in conjugate pairs. The tutorial demonstrates constructing the polynomial function, multiplying factors, and verifying the function by graphing. The example used involves zeros -6, +i, and -i, leading to a cubic polynomial function.

What is a key characteristic of complex zeros in polynomial functions?

• They do not affect the polynomial's degree.

• They are always positive.

• They always come in conjugate pairs.

• They always appear as real numbers.

If a polynomial has a zero at -6, what factor must it include?

• x + 1

• x - 6

• x + 6

• x - 1

What is the conjugate of the complex zero +i?

• 0

• +i

• -i

• -1

Why is it unnecessary to include a constant factor in the polynomial function in this example?

• The binomial factors do not contain fractions.

• The zeros are all complex numbers.

• The zeros are all real numbers.

• The polynomial is already simplified.

When multiplying conjugate pairs, what is the result of i squared?

• 1

• -1

• 0

• i

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

• x^2 + i

• x^2 - 1

• x^2 + 1

• x^2 - i

What is the degree of the polynomial function formed in the example?

• 1

• 2

• 3

• 4

What is the polynomial function's x-intercept based on the given zeros?

• x = 0

• x = -6

• x = +6

• x = 1

What is the polynomial function's term with the highest degree?

• x^4

• x^2

• x

• x^3

How can the zeros of a polynomial function be verified graphically?

• By checking the curvature.

• By checking the slope.

• By checking the x-intercepts.

• By checking the y-intercepts.