Multiplicity and Possible Real Roots of Polynomials

f(x)= x²(x – 2)³(x – 7)

Find and select each real zero and its multiplicity

• 0 (Mult of 2), 2 (Mult of 3), 7 (mult 1)

• 2 (Mult of 3), 7 (mult 1)

• 0, 2, 7

• 2 (mult of 2), 7 (mult of 3)

What are the zeros of the graph?

• -4, -1, 2, 1 multiplicity 2

• -4, -1, 1, 2

• 4, 1, -2, -1 multiplicity 2

• 4, 1, -1, -2

What does multiplicity mean in terms of the roots of an equations?

• To clone a polynomial

• How many times a particular number is a zero for a given polynomial.

• how many times a polynomial function crosses the x-axis

• how many end behaviors a polynomial has

Which of the following statements are true?

• This polynomial has two real roots

• This polynomial has four real roots

• This polynomial has two imaginary roots

• This polynomial has three real intercepts

• 2, 7 multiplicity 3

• -2, -7 mulitplicity 3

• -2, 7 mulitplicity 3

• 2, -7 multiplicity 3

Where is the root with multiplicity of 2?

• between -1 and 0

• 1

• between 2 and 4

• there is no root with multiplicity 2

Which root has a multiplicity of 2?

• -1

• 2

• 4

• -4

Which root has even multiplicity?

• 1
• -4
• -1
• 2

• 7

• 4

• 9

• 2

Find all of the real roots.

• 2, -6

• 6, -2

• -6, 6, 2

• -2, -6, 6