write polynomials with the given roots

Question

I. A third-degree polynomial with roots 2 and 3, with the root 3 having multiplicity 2.

II. a third-degree polynomial with roots 1 and 2i.

Answer 1

Hi Joe

 

multiplicity just means duplicate factors

 

Factors of polynomials appear in the form of (x-a root)(x-another root) and so on

 

So, you have (x-2) and (x-3).

 

Then you take the multiplicity 2 for the (x-3) and you will have (x-2)(x-3)(x-3)

 

 

 

Answer 2

(x - 2)(x - 3)(x - 3) Multiply these together.

( x - 1)(x - 2i)(x + 2i)  Multiply these together.

Remember the difference between solutions and factors. They have signs that are negative of each other.