I read that if the degree of a polynomial equation is odd then the number of real roots will also be odd.
I took the example of a cubic equation. If it has imaginary roots then that will occur in pair. Thus, the cubic will have at least one real root.
But imaginary roots occur in pair when the coefficients are real.
Also, if I look at the graphs of cubic equations, I see that it crosses x-axis at least once, thus it has atleast one real root.
But is it possible that the coefficients are imaginary and all three roots are imaginary?