Fundamental Theorem of Algebra and Multiplicity

How many zeros does the following function have?
f(x)= x⁵ - 3x³ + x

• 8

• 9

• 5

• 3

What is the total number of roots for the following equation?
y = 4x⁶ - 12x⁵ - x⁴ + 2x³ - 6x² - 5x + 10

• 4

• 5

• 6

• 7

State the zeros of the polynomial (include multiplicity):
f(x) = (x²+9)(x -1)³(2x + 5)

• -9, 1, -5

• -9, 1 (multiplicity of 3), -5

• ± 3i , 1 (multiplicity of 3), -5∕2

• ± 3i, 1, -5

A polynomial of degree n has

• only 1 zero

• exactly n zeroes

• at most n zeroes

• more than n zeroes

What statement must be true about the this polynomial?

• It has exactly 3 roots (including repeated roots) and they have to be real numbers

• It has exactly 5 roots (including repeated roots) that may be real or complex numbers

• It has exactly 3 roots (including repeated roots) that may be real or complex numbers

• It has exactly 5 roots (including repeated roots) and they have to be real numbers

• 1

• 3

• 5

• None of the above

Which of the following statements is a direct consequence of the Fundamental Theorem of Algebra?

• Every polynomial of degree greater than zero has at least one real root.

• Every polynomial of degree greater than zero has at least one complex root.

• Every polynomial can be factored into linear factors in the set of real numbers.

• Every polynomial can be factored into linear factors in the set of complex numbers.

What is the Fundamental Theorem of Algebra?

• The degree of the polynomial determines what the x value will be

• The degree of the polynomial tells us how many solutions the polynomial will have.

• States that a complex number and its conjugate are solutions

The degree of the polynomial determines the number of roots.

• True

• False

A Polynomial of Degree 6 CAN have the following number of imaginary roots:

• 1

• 4

• 3

• 8