If the coefficients of the polynomial in question are all real. Then non-real roots must come in conjugate pairs. That's why their number must be even.

The number of real roots doesn't have to be odd though.

$f(x) = (x-1)(x-2)(x-3)(x-4)(x-i)(x+i)$

has 4 real roots and 1 pair of complex conjugate roots

If the coefficients of the polynomial in question are all real. Then non-real roots must come in conjugate pairs. That's why their number must be even.

The number of real roots doesn't have to be odd though.

$f(x) = (x-1)(x-2)(x-3)(x-4)(x-i)(x+i)$

has 4 real roots and 1 pair of complex conjugate roots

Hi, I have read all above forum I have some good information about Algebra there is an app called Algebrator Math Solver Calculator to solve any kind to an algebra math problem

Hi, I have read all above forum I have some good information about Algebra there is an app called Algebrator Math Solver Calculator to solve any kind to an algebra math problem