I have at some point in my calculations a list of numbers, examples being
{1, 140, 4144, 14400}
or
{1, 165, 8778, 172810, 1057221, 893025}
There is also a point where I have a corresponding list
{x^6, -140 x^4, 4144 x^2, -14400}
or
{x^10, -165 x^8, 8778 x^6, -172810 x^4, 1057221 x^2, -893025}
What I would like to do is assemble a solvable equation from either of the list types. So I would either have
Solve[{{x^6 - 140x^4 + 4144x^2 - 14400 ==0},x}]
or
Solve[{x^10 - 165x^8 + 8778x^6 - 172810x^4 + 1057221x^2 - 893025 ==0},x]
The format is always the same in that no matter how many terms there are the parity is always +, -, +, - ... == 0 and the right most term is always a constant and the others reading right to left are x^2, x^4, x^6... etc. Any pointer