Question

Find the complex zeros of the polynomial function. Write f in factored form.
a.) F(x)= x^3-5x^2+11x-15
b.) f(x)=x^4+26x^2+25
c.) F(x) = 3x^4-10x^3-12x^2 +122x-39

Answer 1

too hard
just cheat

Answer 2

for the first one, try \(f(1)\)

Answer 3

\[1-5+11-15\] no that is not zero
try \(f(-1)\)

Answer 4

lol ok

Answer 5

no, ok try \(f(3)\)

Answer 6

you get -18

Answer 7

no you get 0

Answer 8

oh yeah sorry i multiplied wrong

Answer 9

\[f(x)=(x-3) (x^2-2 x+5)\]

Answer 10

find the the other two zeros by setting
\[x^2-2x+5=0\] and completing the square

Answer 11

so the complex zeros are 3, 1-2i, and 1+2i

Answer 12

yes

Answer 13

well 3 is a real root, the other two are complex

Answer 14

\[x^4+26x^2+25\]
\[(x^2+1)(x^2+25)=0\] solve that one in a heartbeat

Answer 15

it was wrong the right answer was ... (x-3)(x-1-2i)(x-1+2i)

Answer 16

oh sorry it changed the question cause i got it wrong

Answer 17

no it was not wrong
they wanted you to write the polynomial in factored form, not just find the zeros

Answer 18

oh sorry

Answer 19

did you get the second one?

Answer 20

yeah i got x=-i,i,-5i,5i

Answer 21

ok good`

Answer 22

so now how do I write that in factored form ?

Answer 23

\[(x+i)(x-i)(x+5i)(x-5i)\]

Answer 24

how did you get the first step?

Answer 25

cause i'm trying to do the third question and i don't know how you approached it

Answer 26

\[c.) F(x) = 3x^4-10x^3-12x^2 +122x-39\] is different because the second one has only \(x^4\) and \(x^2\)

Answer 27

you just have to check what gets zero, it is a pain in the neck
i would cheat
http://www.wolframalpha.com/input/?i=3x^4-10x^3-12x^2+%2B122x-39

Answer 28

so would it just be (3-2i)(3+2i)