Theorems About Roots of Polynomial Equations

Use the Fundamental Theorem of Algebra to state the number of zeros/solutions/roots of the polynomial. 

• A

• B

• C

• D

Tags

CCSS.HSN.CN.C.9

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

• 8

• 9

• 5

• 3

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

• 4

• 5

• 6

• 7

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

• 0

• 4

• -9

• -15

Which of the following roots match the above polynomial:

• -3,-1,4

• -3,2i,-2i

Find the zeros of the polynomial given one factor. Use synthetic division.

• X= 3,4,5

• x=-3,-4,-5

• x=-3,4,5

• x= 3, -4, -5

Tags

CCSS.HSF-IF.C.7C

The nth degree of a polynomial is equal to the number of root that same polynomial has: is a true statement of which theorem?

• Factor Theorem

• Remainder Theorem

• Fundamental Theorem

• All of the above

• None of the above

Which formula is the Fundamental Theorem of Algebra Formula?

• There are infinitely many rationals between two reals.

• Every polynomial equation having complex coefficents and degree greater than the number 1 has at least one complex root.

• There are infinitely many prime numbers.

• All numbers are rational numbers.

Tags

CCSS.HSN.CN.C.9

Use the Fundamental Theorem of Algebra to state the number of zeros/solutions/roots of the polynomial. 

• A

• B

• C

• D

Tags

CCSS.HSN.CN.C.9

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

• 4

• 3

• 2

• 5

Tags

CCSS.HSF-IF.C.7C