Is it true?

Question

suppose two polynomials are there
(a-b)^(n)+nk(a-b)=1
(a-b)^(2)+2c(a-b)=1
as the two polynomials are equal then their coefficients must be equal so nk=2c.
Is it true?

Answer 1

i think, its partially true.

let a-b=x
no.1=> x^n+nkx-1=0
no.2=> x^2+2cx-1=0

eqn no.1 has n solutions that means a-b has n values for which (a-b)^(n)+nk(a-b)=1
depending on the value of k and n u can get complex results. but u'll certainly get n results.

eqn no. 2 has 2 solutions only that means a-b has 2 values only for which
(a-b)^(2)+2c(a-b)=1

your assumtion is true only in case of n=2, but having other n's will bear other results, and certain conditions cant be found for which u can claim that it is possible only for n=2

[I've have assumed k and c as unequal constants]

Answer 2

The two polynomials are equal only when n=2 and k=c, both are real, however it need not be sufficient condition for it to be true. For eg, if n is not equal to 2 or k and c are complex, then the two polynomials are not equal.

Answer 3

In this case it is true as we can compare the coefficients of the variable terms(assuming c is also a constant like k).

Answer 4

yes thats definately true.
nk = 2c, you're right.

Answer 5

I think it should be true,to the extent of 100 per cent.

Answer 6

Yeah it means k=c, since n=2.

Answer 7

True

Answer 8

Yes its true

Answer 9

yes it is true

Answer 10

I dont know what is true.But what i said is true.