Question

how to write a polynomial equation with given roots -1, 3±i, 2±3i

Answer 1

in general for these problems do these steps:
-- assign each root equal to "x"
-- work backwards to get one side to be zero
-- the other side will be a "factor" of the polynomial

Answer 2

note: to get rid of the "i" you would square both sides

Answer 3

let Q be that set of complex numbers, then $$\prod_{a\in Q}(x-a)$$ Is a polynomial with those roots.

Answer 4

omg can you guys give me steps TAT i dont get anything from you guys right now

Answer 5

example
\[x = 3\pm i\]
\[x-3 = \pm i\]
\[(x-3)^{2} = i^{2} =-1\]
\[(x-3)^{2} +1 = 0\]
\[x^{2}-6x+10 = 0\]

Answer 6

oh god you are wow ok thanks so much i got this i got this

Answer 7

yw, make sure you multiply all the factors at the end to get polynomial with a "x^5" in it

Answer 8

what did you say?

Answer 9

they gave you 5 roots, so the answer should be a 5th degree polynomial

Answer 10

oh ok haha

Answer 11

can you guys give me the answer so i can solve this multiple time

Answer 12

i thought you said you "got this"
i will check your answer for you, if you do the rest of the work

Answer 13

ok i will try

Answer 14

tell me what you get for the roots: 2+-3i

Answer 15

x^2-10x+23

Answer 16

ok i have
x^2 -4x +13

can you show your steps and ill tell you where you messed up

Answer 17

oh sorry i type worng that was right

Answer 18

i typed wrong one

Answer 19

so whats next step

Answer 20

i think i got the final answer can you check it

Answer 21

yep

Answer 22

2x^3-12X^2+33x-23

Answer 23

no thats not even remotely close??
remember the 5 roots , 5th degree thing

Answer 24

how can it form 5 roots...

Answer 25

oh i got it

Answer 26

wait teacher wait

Answer 27

x^5-14x^4+57x^3-165x^2+248x-130

Answer 28

i hope it does...

Answer 29

that looks better but coefficients are off, let me verify you started with this right
\[(x+1)(x^{2}-6x+10)(x^{2}-4x+13)\]

Answer 30

no... its x-1 what r u talking about....

Answer 31

-1 is the root
\[x = -1\]
\[x+1 = 0\]
(x+1) is the factor

Answer 32

so.. really. i gotta change that too? root thingy?

Answer 33

yeah

Answer 34

ok i got the answer check it out

Answer 35

x^5-8x^4+x^3-58X^2+12x+130

Answer 36

the "12x" is correct
should be:
\[x^{5}-9x^{4}+37x^{3}-71x^{2}+12x+130\]

Answer 37

wow.............

Answer 38

what did you multiply by last one

Answer 39

\[(x+1)(x^{2}-6x+10)(x^{2}-4x+13)\]
\[(x^{3}-5x^{2}+4x+10)(x^{2}-4x+13)\]

Answer 40

hey you solve wrong sigh.........................

Answer 41

??

Answer 42

wtf you solved wrong..........

Answer 43

what do you mean i solved wrong?
are you saying you disagree with the solution

Answer 44

(x+1)(x2−6x+10) dont you multyply these

Answer 45

yes correct
the next line shows the result

Answer 46

its x^3-4x^2+4x+10.............. RU OK

Answer 47

http://www.wolframalpha.com/input/?i=%28x%2B1%29%28x%5E2-6x%2B10%29

Answer 48

when you expand you should have -6x^2 +x^2 = -5x^2

Answer 49

how to expand,,, so tired sorry..

Answer 50

expand, multiply, distribute its all the same thing