Prove that the equation `Z^3+i Z-1=0` has no real roots.

The equation Z^(3)+iZ-1=0 has

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

For a complex number z, the equation z^(2)+(p+iq)z r+" is "=0 has a real root (where p, q, r, s are non - zero real numbers and i^(2) = -1 ), then

Show that the equation Z^(4)+2Z^(3)+3Z^(2)+4Z+5=0 haly no root which is either purely real or purely imaginary.

If the equation ax^(2)+bx+c=0 has non-real roots,prove that 1+(c)/(a)+(b)/(a)>0

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.

The quadratic equation z^2 +(p+ip')z+q+iq' =0 where p,p',q,q' are all real. (A) if the equation has one real root then q'^2-pp'q'+qp'^2=0 (B) if the equation has two equal roots then pp'=2q' (C) if the equation has two equal roots then p^2-p'^2=4q (D) if the equation has one real root then p'^2-pp'q'+q'^2=0

One of the roots of a quadratic equation with real coefficients is (1)/((2-3i)) . Which of the following implications is/are true? 1. The second root of the equation will be (1)/((3-2i)) . 2. The equation has no real root. 3. The equation is 13x^(2)-4x+1=0. Which of the above is/are correct ?

The number of real roots of the equation z^(3)+iz-1=0 is

Find the range of real number alpha for which the equation z+alpha|z-1|+2i=0 has a solution.