Question

Help Please!!
Suppose that R (x) is a polynomial of degree 7 whose coefficients are real numbers.

Also suppose that R(x) has the following zeros: -2 + I, 2i

Answer the following:
A. Find another zero of R(x)
B. What is the maximum number of real zeros that R(x) can have?
C. What is the maximum number of non-real zeros that R(x) can have?

Answer 1

complex zeros come in conjugate pairs

Answer 2

So for imaginary numbers it's the same? so I would take -2+i, and 2i there would be 2 more zeros> -2-i and -2i? answer for A. really confused with the imaginary numbers in the equation.

Answer 3

if (a+bi) is a complex zero of a polynomial, then so is (a-bi).

they give you 2 different complex zeros, which means that we have 4 that we can account for.

a 7 degree poly has at most 7 zeros total.

Answer 4

yes,

Answer 5

According to Fundamental Theorem of Algebra, two another zeros are the conjugate of -2+i and 2i, which is -2-i and -2i.

Answer 6

My answer for 'A' would be. -2-i, and -2i correct?

Answer 7

we can make a table of zeros :)

z1 z2 z3 z4 z5 z6 z7
-2i 2i -2+1 -2-1

we can fill in the rest of the table with either 3 real zeros and 0 complex zeros


z1 z2 z3 z4 z5 z6 z7
-2i 2i -2+1 -2-1 a b c


OR we can fill it in with 1 real zero and 2 complex zeros (since they come in pairs)


z1 z2 z3 z4 z5 z6 z7
-2i 2i -2+1 -2-1 a+bi a-bi c

Answer 8

For question 'B'. The maximum number of "real" zeros would be the maximum numbers of degrees stated which is "7". So there are "7" real zeros correct?

Answer 9

there cant be 7 real zeros if we already know that 4 are complex (imaginary)

Answer 10

aaahhh so for question A- the total number of real zeros are the total sum of the complex (imaginary). -2+i, 2i, -2-i, and -2i...

Answer 11

Sorry amistre this is just hard to wrap my head around.

Answer 12

for "A" that would be the set of the total number of KNOWN complex zeros, yes

Answer 13

so another zero would be what is NOT stated which is -2-i, and -2i.

Answer 14

if we only focus on A at the moment, then that is correct. Another zero that we can be sure of is either: -2-i OR -2i

both are acceptable results

Answer 15

Awesome!!

Answer 16

and for B. to find the maximum number of Real Zeros I would take the degrees given "7" and subtract the "known" zeros "4" to give me 3 real zeros.

Answer 17

correct, there are only 3 zeros left, and they can all be filled with real numbers.

Answer 18

You are a math genius- Finally I'm starting to get it.

Answer 19

thnx :)

Answer 20

For the Non- Real zeros... The only possibilities I have are complex... So I have "4" complex numbers and 3 real numbers. My answer would be 6 non-real zeros?!?!

Answer 21

For the Non- Real zeros... The only possibilities I have are complex... So I have "4" complex numbers and 3 real numbers. My answer would be 6 non-real zeros?!?!

Answer 22

yes, why? we know 4 complex already. and since complex zeros come in pairs, we can only fit 2 more UNKNOWN complex zeros inthe remaing spaces.

4+2 = 6 complex zeros max

Answer 23

so the total number of complex numbers are all non-real zeros? Totaling 6

Answer 24

correct

Answer 25

WOW!!! I've been working on this for days- you are Great!! Just to sum it up
A. -2-i, or -2i
B. 3 real zeros
C. 6 non real zeros

Answer 26

that looks good to me :)

Answer 27

tytytytyty!! I'm your fan :)

Answer 28

good luck ;)

Answer 29

Not sure how I do the medal thing on here...