Question

Four roots of a polynomial are 2, 4+i, 5-3i, and -2i. Which number is NOT necessarily a root of the equation?
A) -2
B) 5+3i
C) 2i
D) 4-i

Answer 1

Recall that complex roots always come in pairs.
If 5-3i is a root of this polynomial, then it's conjugate 5+3i must also be a root.

Answer 2

Can you use that logic to determine anything about the 4+i root?

Answer 3

4+i is not a root?

Answer 4

i have no idea

Answer 5

These are the given roots:
2, 4+i, 5-3i, and -2i

We determined that 5-3i has a buddy, because it's a complex number.
4+i is also a complex number, yes?

Answer 6

yes

Answer 7

so the answer is 2?

Answer 8

So his conjugate MUST be a root as well.
4-i.

Answer 9

2 is not one of your options.
I'm not sure what you mean.

Answer 10

-2
i meant

Answer 11

Yes good job.
Real roots don't necessarily come in pairs.
So the 2 root doesn't tell us anything about any other real roots.

Answer 12

thank you!!!