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:

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.

Prove that the equation 3x^(5)+15x-18=0 has exactly one real root.

If the equation ax^2 + bx + c = 0, 0 < a < b < c, has non real complex roots z_1 and z_2 then

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 the equation ax^(2) +bx+c=0, 0 lt a lt b lt c , has non real complex roots z_(1) and z_(2) then

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

One root of the equation ax^(2)-3x+1=0 is (2+i) . Find the value of 'a' when a is not real.