Question

please help!!!!!

find all real and imaginary solutions

-2x3 + 4x^2 +2x -4 = 0

Thank you so much!

Answer 1

by inspection \(f(1)=0\)

Answer 2

I want to learn but I don't know where to start :-/

Answer 3

factor as \(-2x3 + 4x^2 +2x -4=(x-1)(something)\)
the something will be quadratic, solve using the quadratic formula if you can't factor it

Answer 4

i made a guess
i guessed \(f(1)=0\) and i was right

Answer 5

i'm still confused how do I solve this?

Answer 6

hmmm... you know how to do long division for polynomials, right?

Answer 7

no sorry...

Answer 8

can I factor?

Answer 9

do you know synthetic division?

Answer 10

no i'm not sure

Answer 11

how do I

Answer 12

What method(s) were taught in your class? I mean, there are different ways to do this, but it would help to know what your instructor is expecting, as that will indicate what has been covered and what you should be familiar with.

Answer 13

It's a 3rd degree polynomial, which means that it has exactly 3 roots (when considering both real and complex roots). So it can be factored into something of the form:

\(a(x-c_1)(x-c_2)(x-c_3)\) where the c's are the 3 roots.

Answer 14

he barely touched on this but he used synthetic division. Unfortunately I have no clue how to o it O.o

Answer 15

What @satellite73 was getting at above is, once you find ONE of those roots - it doesn't really matter which one (but a real, rational root is the easiest to find), then you can factor that out and what you are left with is a quadratic. Those, we know how to handle.

Answer 16

OK, I'll show you, but you might also need to refer to your textbook and class notes, read and re-read, and do some practice example. Contrary to what many math students want to believe, this stuff doesn't sink in my osmosis! ;) lol

But here we go: you start with your polynomial: \(\Large -2x^3 + 4x^2 +2x -4\)

Now, SOMEHOW you find that first, rational root. there is something called the "rational root theorem" that can help you narrow it down, or you might be able to graph the function and inspect the graph to detect your "first root".

since we already know that 1 is a root, we'll work with that. So we are starting with c=1, which gives us a factor of x-1

Answer 17

ohhh so u split it up into (-2x^3 +4x^2) and (2x-4)?

Answer 18

and x=2?

Answer 19

Now we are going to do synthetic division, to find the QUOTIENT and REMAINDER, when we divide:

\(\Large (-2x^3 + 4x^2 +2x -4) \div (x-1)\)

Of course, since we believe that 1 is a root, we are expected a remainder of 0. We set up the synthetic division by putting the COEFFICIENTS of our polynomial, in order, in an upside down "box", and then we put our value for c (in this case, c=1) on the outside, like so:

Answer 20

(no, not what you said, sloooow down, one step at a time! lol )

Answer 21

That's just my set-up... do you follow everything so far? understand where I got all the numbers involved?

Answer 22

ess they're the coefficiets

Answer 23

but were do you get (x-1)?

Answer 24

Now I'm going to just bring down the first number, then multiply THAT by the c, and put it under the 2nd coeff in the box: