Question

Find the Complex Roots: 4x3 + 5x2 – x + 2. Thank you!

Answer 1

try using the quadratic formula

Answer 2

alright. let me try this out.

Answer 3

ok take your time

Answer 4

how would it work considering the first term is cubed, not squared?

Answer 5

Look for a simple substitution that eliminates the quadratic term of 4 x^3+5 x^2-x+2.
Eliminate the quadratic term by substituting y = x+5/12:
29/12+5 (y-5/12)^2+4 (y-5/12)^3-y = 0

Answer 6

how would that help?
i don't understand.

Answer 7

i know it simplifies to 4y3 - 37y/12 + 2.99.

Answer 8

@hartnn ?

Answer 9

do you have an easier way of explaining this?

Answer 10

let me think...

Answer 11

That is definitely not one of the options in this multiple choice question.

Let me give the possible answers: (all negative and positive of this number)
a. 1, 1/2, 1/4, 2
b. 1, 1/2, 2, 4
c. 1, 1/2, 1/4
d. 1, 1/4, 2

Answer 12

lol.. wow thats neat work... @pathosdebater

Answer 13

Is the problem 4x3 + 5x2 – x + 2 or 4*3 + 5*2 – x + 2? (Just making sure)

Answer 14

It's exponential, yeah. 4x^3 + 5x^2 - x + 2.

Answer 15

What? Oh... I didn't know that.
I thought it was 4x*3 + 5x*2 - x+2

Answer 16

One second

Answer 17

Sorry for the confusion.

Answer 18

This is so strange. I keep getting irrational answers.

Is there anything wrong in my calculations which could be causing this?

Answer 19

u have an easy way of solving....firstly...note that a cubic eqn has atmost two complex sol..and atleast 1 real soln....so go for the real soln by trial and error...then u hav a factor...divide the polynomial by the factor...u have a quad eqn now as the quotnt....solve it to get the complex roots

Answer 20

@pathosdebater I'm not sure, I got similar answers (which is why I came here). There may be a typo in the question (not what I typed; the actual question itself), but no one I know has said anything about it. :\

Answer 21

What textbook is it?

Answer 22

It's not a textbook, it's a practice given by the teacher. (I searched online for duplications but it looks original.)

Answer 23

Hmm... well there are definitely only 3 roots, so that narrows it down to C and D.

Answer 24

Thanks for the help though, I'm just going to guess. I appreciate the effort.

Answer 25

I got it! It is definitely C

Answer 26

do u mind if i say that the options, all of them are wrong..? its so coz...u cant have three complex roots for a REAL cubic eqn...complex roots come in pairs...so...

Answer 27

That was my initial guess, but can you explain how?

Answer 28

2 is not a complex root

Answer 29

Let me see if I can try and explain...

Answer 30

its got to have two complex roots ..if not zero

Answer 31

@amriju I don't mind, I found it to be that way too when I substituted it in. I don't know. Not my practice, it was the teachers. I got all of the other questions on finding zeros, this one was just confusing.

Answer 32

have u done complex numbers @pathosdebater

Answer 33

Only briefly. I'm not a wizard at them... yet

Answer 34

u really cant have an option with more than two values...that settles it...as for the solution u got to try this way...if a,b,c be the roots then\[\sum_{?}^{?} a=-5/4...\sum_{?}^{?} ab=1/4....abc=-2/4=-1/2\]