Question

Given that the following roots are roots of a polynomial, what other roots canyou assume also exist? *-5, 2-V5 and -3i

Answer 1

The possible roots are;

`3i\text{ , 5 and 2+}\sqrt[]{5}`

Here, we want to get the possible other roots

Now, we start from the complex root;

This is -3i

Mathematically, we can have that as;

`\sqrt[]{-9}\text{ and the roots are -3i and 3i}`

That means 3i is a possibe root

Furthermore, we can have;

`2+\sqrt[]{5}`

This is because the root of 5 can be positive and negative

Lastly, we can have the positive value of 5, given that we do not have the degree of the polynomial to ascertain the possible number of roots