- #1
eljose
- 492
- 0
All the roots of a real function f(x) are real unless.
1.K(x) is a Polynomial of degree k
2.f(x)=exp(g(x)) where g(x) is different from ln of something
3.f(z) with z=u+iv is invariant under the transformation of v=-v with f(u+iv)=F(u-iv)..
4.the function f includes some of the functions above named
In this cases there can be complex roots,excluding this all the roots are real...
1.K(x) is a Polynomial of degree k
2.f(x)=exp(g(x)) where g(x) is different from ln of something
3.f(z) with z=u+iv is invariant under the transformation of v=-v with f(u+iv)=F(u-iv)..
4.the function f includes some of the functions above named
In this cases there can be complex roots,excluding this all the roots are real...