Question

Check my answer? List possible roots for the equation 3x^4 - 5x^2 + 25 = 0

A. +1, +5, +25
B. +1, +1/3, +5, +5/3, +25, + 25/3
C. +1, +3
D. +25/3

I think it's A

Answer 1

are u sure u write it correctly?
i mean the question

Answer 2

just take one of the root instead of x there will be no answer

Answer 3

Yes its written exactly how the question is asked @M_A

Answer 4

but there is no answer
could u tell me how u find A?

Answer 5

the school wouldn't give me a question there is no answer to

Answer 6

i'm really sorry
maybe i dont get your question

Answer 7

To start, this is a quartic, so you cannot have 6 roots.
The product of the roots must equal 25/3, and in no case it satisfies that, even if we assume double roots somewhere.
You may have mismatched the question and the answer. @JoeJoldin
I have to agree with @M_A.

Answer 8

thanks mathmate

Answer 9

it says possible roots
they are using that one test..
what's it called
rational root test

Answer 10

thought the wording of the question is weird

Answer 11

because it doesn't say list the possible rational roots

Answer 12

it says list the possible roots

Answer 13

but based on the choices it looks like it wants us to apply that rational root test/theorem whatever it is called

Answer 14

you find the factors of the coefficient with least degree
and find the factors of the coefficient with most degree
the possible rational zeros will be:
the factors of the coefficicent with least degree union the factors of the coefficient with least degree over the factors of the coefficent with most degree

Answer 15

and I bet she means + or -

Answer 16

Yes, I agree, you read the question right.
"Possible" roots is the key. So use the rational root theorem!

Answer 17

Yes I need the rational roots please

Answer 18

for example if you have
10x^3-x^2-14x+4

you find factors of 4: (image I say + or - on each of these numbers ) 1,2,4
find factors of 10: (image I say + or - on each of these numbers) 1,2,5,10
the possible rationals are therefore (image I say + or - on each of these) 1,2,4,1/2,1/5,1/10,2/5,4/5,2/5

All I did was exactly what I said above (and I maye reduced)

Answer 19

oops don't need to list 2/5's twice

Answer 20

you already found the factors of 25
you need to find the factors of 3
the answer will be the factors of 25 union the factors of 25 over the factors 3

Answer 21

So the answer is B? @freckles

Answer 22

B is definitely tons cute to me

Answer 23

so...yes? @freckles

Answer 24

@freckles

Answer 25

@JoeJoldin
According to the rational root theorem, the possible roots are:
\(\pm \frac{possible~factors~of~the~constant~term}{possible~factors~of~the~leading~coeefficient}\)
Leading coefficient is the coefficient of the hightest power of the polynomial.
Example:
The possible roots of
\(6x^2-x-15\) are \(\pm\frac{1,2,3,6}{1,3,5,15}\) for a possible total 32 possibilities, such as 1/1,1/3,1/5,1/15,2/1,2/3,2/5,2/15,3/1,(3/3),3/5,(3/15),6/1,(6/3),6/5,and (6/15), all have either plus or minus.