Question

What is the least possible degree of a polynomial that has roots -5, 1 + 4i, and -4i?

2
3
4
5



how do i go about this
would it be 4?

Answer 1

or three actually

Answer 2

the 1 + 4i and 4i are complex and imaginary numbers respectively.

these 2 roots occur as conjugate pairs which means there is another 2 roots 1 - 4i and -41

Answer 3

so how many are there?

Answer 4

another two added onto that one .......if not would it be four than

Answer 5

nvm i mean 5 sorry

Answer 6

??

theres -5 , 1+4i and 4i in the question

Answer 7

yes 5

Answer 8

its takes a few trys for me to get things into my head correctly sorry

Answer 9

i have to read it over and over and over again before i can finally understand wht it says

Answer 10

thats ok.

Answer 11

thanks for the help

Answer 12

@dirtydan667 omg you're username was my imaginary friend when i was little except for the 667, dirty dan was my best friend lmfao

Answer 13

The polynomial p(z)=(z+5)(z−(1+4i))(z+4i) has exactly those 3 roots. And the equation p(z)=0 has exactly 3 roots. Not 5. The "conjugate" argument used above would hold for 2nd order equations.

Actually, this is true if the coefficients are allowed to be complex.
If they are only real numbers, my argument my fail..
Is the statement of the problem specific about the type of coefficients? (real numbers/complex numbers)

Answer 14

yes I assumed that the coefficients were all real.