The Fundamental Theorem of Algebra

Which of these is a possible root of the polynomials?
x³ - 6x² - x + 30

• 0

• 4

• -9

• -15

Find all the roots of y=x³-2x²+4x-8

• -2, 2i, -2i

• 2, 2i, -2i

• 2,-2, 2i

• 1, 2i, 4

Find all the roots of y=x³+x²-x+2

• -2, (1±i√3)/2,

• 2, (1±√3)/2,

• 2, (1±i√3)/2,

• -2, (-1±i√3)/2,

Identify the number of roots:
x³+4x²-11x-30

• 1

• 2

• 3

• 4

• 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.

• The number of possible rational zeros

• States that a complex number and its conjugate are solutions

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

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

• 4

• 5

• 6

• 7

The degree of the polynomial determines the number of roots.

• True

• False