Question

A polynomial equation has only imaginary roots and no real root. Which options CANNOT be the degree of that polynomial? (Select all that apply.)

A. 2
B. 3
C. 4
D. 6
E. 7
F. 8

Answer 1

Options B and E

Explanation:

Given that a polynomial equation has only imaginary roots.

Since the polynomial has real coefficients, the imaginary roots can only occur in pairs as each conjugate of the other.

In other words, the polynomial can have only an even number of imaginary roots.

Since all roots are imaginary, the polynomial can have degrees as even number only

either 2 or 4 or 6 or 8

It is not possible for the polynomial to have degrees as 3,7

Hence answers are

options B and E

Answer 2

we know that

Imaginary roots will come in pairs, and so the degree must be even.

therefore

the answer is

options

`B. 3`

`E. 7`