If x-a is a factor of the difference of powers of equal odd exponent of the form x^(n)-a^(n) the signs of the second factor are: A. All negative B. All positive C. Alternating +…

Question

If x-a is a factor of the difference of powers of equal odd exponent of the form x
`^(n)`-a
`^(n)` the signs of the second factor are:

A.
All negative

B.
All positive

C.
Alternating +, -, + ...

Answer 1

Option 'D' is correct.

Explanation:

Since we have given that

Both the first and second signs are negative,

Let α and β are the roots of the ,

then, we know that the relationship between the zeroes and coefficients of quadratic equations:

Since the product of roots is positive.

So, the signs of the factors will be one positive and one negative.

Hence, Option 'D' is correct.