Question

Find all roots of the polynomial

f(x)= x^4-3x^3+4x^2-6x+4

Answer 1

do you mean +4 at the far end there?

Answer 2

Yes! oops!

Answer 3

hmm okay..are you familiar with remainder theorem and rational roots theorem? or no?

Answer 4

No :/

Answer 5

then i guess you have to factor this out the hard way...you know how to do long division right?

Answer 6

Yes

Answer 7

hmm are you sure this question is right? im not getting a factored form... :/

Answer 8

Nope I messed up I apologize

Answer 9

lol =))))

Answer 10

There is the re-re-edited

Answer 11

ahh better...okay...start by dividing it by x-2 and tell me what you get

Answer 12

I'm reading about the factor therorem

would my division look like this

\[2 1 1 0 0 \div -2\]

Answer 13

hmm?

Answer 14

I'm most likely very wrong

Answer 15

where did you get 2110 / -2?

Answer 16

the factor theorem is that if x - 2 is a factor that means f(2) = 0

Answer 17

I'm trying to look at an example in my book, but I'm failing

Answer 18

here's an example..

x^2 - 2x + 1

i want to know the factors to this using factor theorem

i'll try x + 1

so if f(-1) = 0 that means x + 1 is a factor

f(-1) = (-1)^2 - 2(-1) + 1
f(-1) = 1 + 2 + 1
f(-1) = 3

it's not 0 so x+ 1 is not a factor.

now i'll try x - 1

if x - 1 is a factor f(1) should be 0

f(1) = (1)^2 - 2(1) + 1
f(1) = 1 - 2 + 1
f(1) = 0

that means x - 1 is a factor of x^2 - 2x + 1

make sense?

Answer 19

Yeah