could any one say the possible roots of the equation

Question

(x^7)-(x^5)-(x^4)-6(x^2)+7=0,
 
and also please say how to solve this.....

Answer 1

Note that the constant 7 is only 1 away from the coefficient of x². By substituting x=1, the first two terms cancel out and we get:

1-1-1-6+7=0. And when x=-1 we get -1+1-1-6+7=0. That gives us two zeroes: x=1 and x=-1.

We could divide the polynomial by the factors x-1 and x+1 to reduce the degree of the polynomial and find more zeroes (there should be at least one more).