Consider the equation `z^(2)-(3+i)z+(m+2i)=0(mepsilonR)`. If the equation has exactly one real and one-non-real complex root, then which of the following hold(s) good:

The equation z^2 - (3 + i) z + (m + 2i) = 0 m in R , has exactly one real and one non real complex root, then product of real root and imaginary part of non-real complex root is:

Prove that the equation x^(3) + x – 1 = 0 has exactly one real root.

Let z be a complex number satisfying the equation z^(2)-(3+i)z+m+2i=0, wherem in R Suppose the equation has a real root.Then root non-real root.

If the equation ax^(2)+bx+c=0,0

If omega is a complex non-real cube root of unity, then omega satisfies which one of the following equations ?

Prove that the equation,3x^(3)-6x^(2)+6x+sin x=0 has exactly one real root.