Equal roots of a certain polynomial equation by changing the sign?

Question

Is there a certain polynomial equations which when you change the sign of the equation the roots will still be the same? I wonder if there are, how can it be constructed using the algebraic properties?

Answer 1

In general if $$f(x)=f(-x)$$ the function $f$ is termed an even function.

Examples, $$f(x)=x^4+x^2+1$$ $$f(x)=cos(x)$$ You can recognise such functions from their graphs because they have reflectional symmetry in the y-axis.

Does that answer your question ?