Question

Using the given zero, find one other zero of f(x). Explain the process you used to find your solution.

1 - 2i is a zero of f(x) = x4 - 2x3 + 6x2 - 2x + 5.

Answer 1

there is a theorem that states 'if a+bi is a zero, then a-bi is also a zero of a function with real co-eff'
so if 1-2i is a zero, 1+2i is also a zero of f(x), let me find out the name of that theorem

Conjugate Pair Theorem:
If a polynomial has real coefficients then any complex zeros occur in complex conjugate pairs. That is, if a + bi is a zero then so is a – bi, where a and b are real numbers.

Answer 2

alright, so this is what you sent me

Answer 3

yes.

Answer 4

alright so.

Answer 5

Conjugate Pair Theorem:
If a polynomial has real coefficients then any complex zeros occur in complex conjugate pairs. That is, if a + bi is a zero then so is a – bi, where a and b are real numbers.

so if 1-2i is one of the zeros, then according to Conjugate Pair Theorem, 1+2i is another zero

Answer 6

okay

Answer 7

sooo now what

Answer 8

the question asked for other zero, and u got it as 1+2i, using a theorem.....

Answer 9

oh okay. so thats it?

Answer 10

do i have to plug that in or anything

Answer 11

i guess so, i don't see anything to work out here....

Answer 12

do u have s0lved example of a similar question ?

Answer 13

no

Answer 14

plugging in 1-2i is of no use.

Answer 15

ookay