Complex Zeros and Polynomial Functions Quiz

What is the result of applying the quadratic formula to the equation x^2 - x + 1 = 0?

• x = 1 ± √3/2

• x = 1 ± i√3/2

• x = 1 ± √-3/2

• x = 1 ± i/2

Which of the following is a property of complex conjugates?

• They have the same real part but opposite imaginary parts.

• They are always imaginary numbers.

• They have opposite real parts and the same imaginary part.

• They are always equal.

If 3i is a zero of a polynomial, what must also be a zero?

• 0

• -3i

• 3

• -3

How do you determine a factor of a polynomial if you know one of its zeros?

• Divide x by the zero.

• Multiply the zero by x.

• Add the zero to x.

• Subtract the zero from x.

What is the effect of multiplying a polynomial by a constant on its zeros?

• It removes some zeros.

• It does not affect the zeros.

• It adds new zeros.

• It changes the zeros.

What is the specific condition given in Part B of the polynomial function problem?

• The function must pass through the point (-1, 5).

• The function must pass through the point (-1, 0).

• The function must pass through the point (0, 5).

• The function must pass through the point (1, 5).

What is the maximum number of distinct complex zeros a third-degree polynomial can have?

• Four

• Five

• Two

• Three

What does the degree of a polynomial indicate about its zeros?

• The degree indicates the minimum number of distinct complex zeros.

• The degree indicates the maximum number of distinct complex zeros.

• The degree indicates the maximum number of distinct real zeros.

• The degree is unrelated to the number of zeros.

What is included in the term 'complex zeros'?

• Neither real nor imaginary numbers

• Only imaginary numbers

• Only real numbers

• Both real and imaginary numbers

What will be discussed in the next video according to the transcript?

• How to find more zeros than the degree of the polynomial.

• When a polynomial can have fewer zeros than its degree.

• How to decrease the degree of a polynomial.

• How to increase the degree of a polynomial.