Form a polynomial

[alyren]

Degree 4; zero:3, multiplicity 2; -i

what is the meaning of multiplicity 2?
(x-3)(x-2)(x-i)(x+i) is this right?

 

[mmm4444bot]

Degree 4; zero:3, multiplicity 2; -i

what is the meaning of multiplicity 2?

It means that the given function zero occurs twice.

Or, said another way, it means that the fourth-degree polynomial has a repeated root.

Or, said another way, it means that there will be a squared factor in the function definition.

EGs

(x - 4)(x - 4)(x + 3)

The roots of this polynomial are:

4, multiplicity 2

-3, multiplicity 1

(x - 4)(x - 4)(x - 4)(x + 3)(x + 3)

The roots of this polynomial are:

4, multiplicity 3

-3, multiplicity 2

(x + 2)(x - 3)(x - 7)

The roots of this polynomial are:

-2, multiplicity 1

3, multiplicity 1

7, multiplicity 1



(x-3)(x-2)(x-i)(x+i) is this right? Almost.

Change the 2 to 3, and write the repeated factor as (x - 3)^2.

You recognized that i must also be a zero. Good for you.

The given information could just as well have read:

Degree 4; zero: 3, multiplicity 2; -i, multiplicity 1

Cheers ~ Mark