Question

Write a polynomial of minimum degree in standard form with real coefficients whose zeros include those listed.

5 and 3+2i

Answer 1

Do I set this up as:

(x+5)(3+2i)

Answer 2

@amistre64

Answer 3

if 5 is a zero of polynomial, then (x-5) is one factor

Answer 4

So, (x-5)(x+5)(3+2i)(3-2i) ?

Answer 5

only complex zeroes come in pairs, not real ones

Answer 6

So, what does that mean?

Answer 7

since 3 + 2i, is a zero, 3-2i is also a zero.

so, (x- (3+2i)) and (x - (3-2i)) are factors of the polynomial

Answer 8

since 5 is also a zero, you have (x-5) as another factor

Answer 9

Okay, so only (x-5) and not (x+5)?

Answer 10

thats right !

Answer 11

So, the polynomial will be (x-5)(x-(3+2i)(x-(3-2i)) after being foiled?

Answer 12

Perfect !

Answer 13

Okay, so foil those and then my answer is whatever I get?

Answer 14

hmm wait a sec plz im not getting real coefficients .. .we may need @amistre64 help

Answer 15

Okay.

Answer 16

(3+2i) is a zero, not a factor

Answer 17

and since all complex numbers come with a conjugate

(x-5) (x-(3+2i) (x-(3-2i)) should be the factors right?

Answer 18

Yes.

Answer 19

just did a quick wolf on it, and it works out; ganesh, just check the algebra :)

Answer 20

Is it x^3-11x^2+43x-65 ?

Answer 21

x -3 -2i
x -3+2i

.... yes

Answer 22

ohh yes i see thnks :D

Answer 23

I didn't figure that out... it's the answer the book gives me. Still don't know how to get it after finding zeros

Answer 24

x -3 -2i
x -3+2i
---------
x^2-3x-2ix
-3x +9+6i
2ix -6i -4i^2
----------------------
x^2-6x +9 -4i^2
^^^ = 4

x^2 -6x +13
x -5
------------
x^3 -6x^2 +13x
-5x^2 +30x -65
-------------------
x^3-11x^2+43x -65

Answer 25

"FOIL" is a memory aid, and is not very good at things that have more than 2 terms each. the real math is to simply do multiplication like you was taught in the 3rd grade

Answer 26

i tend to have a left to right appraoch for polys; it just helps me keep track of things easier

a right to left approach is fine as well if that makes you more comfortable

Answer 27

Okay. But I'm getting the same thing using foil.

Answer 28

"FOIL" in this case would, as long as you define what you are using for you terms, would be fine. i just feel it gets a bit convoluted

Answer 29

Okay, and I get what you mean. But thanks for the help, it's greatly appreciated!

Answer 30

youre welcome