Two roots of a polynomial equation with real coefficients are 2 + 3i and .?

Question

*below is full question

6. Two roots of a polynomial equation with real coefficients are 2 + 3i and . Find two additional roots. Then find the degree of the polynomial.

a.) 2 -4i, -√8;Degree 2
b.) 2 -3i, √7;Degree 4
c.) 2 -3i, -√7;Degree 4
d.) 2 +4i, -√9;Degree 12

10 points to best answer, please& thank you!

Answer 1

Two roots are 2 ± 3i since complex roots of polynomials with real valued coefficients must always appear in conjugate pairs. If there are only two additional roots, the polynomial must be of degree 4. There isn't enough information given to determine the additional roots:



The polynomial would be:

(x - 2 + 3i)(x - 2 - 3i)(x - g)(x - h)

where g and h are the two additional roots.



From the multiple choices given, the choice could be either b) or c) if g = h and the polynomial were:

(x-2+3i)(x-2-3i)(x-g)² and g were either √7 or -√7

Answer 2

your question is suppose to say ; Two roots of a polynomial equation with real coefficients are 2 + 3i and √7. Find two additional roots. Then find the degree of the polynomial.



you left out the √7 .

Answer 3

You are missing some information.



You say "with real coefficients are 2+3i and ". What comes after and? This is what we need to answer the question.



If 2+3i is a root, then so is 2-3i, but again, we need additional information (the root after "and")

Answer 4

there is not enough information to determine the other roots