Roots are complex (or imaginary) when D is negative.

Roots are real only when D is non-negative.

If p and q are positive then the roots of the equation x^(2)-px-q=0 are- (A) imaginary (C) real & both negative (B) real & of opposite sign

When the roots are complex they are in conjugate pairs as if one root is p+iq , the other root will be p-iq . Here iq is the imaginary part of the root.

Consider the equation 10 z^2-3i z-k=0,w h e r ez is a following complex variable and i^2=-1. Which of the following statements ils true? For real complex numbers k , both roots are purely imaginary. For all complex numbers k , neither both roots is real. For all purely imaginary numbers k , both roots are real and irrational. For real negative numbers k , both roots are purely imaginary.

Let alpha and beta be two distinct complex numbers, such that abs(alpha)=abs(beta) . If real part of alpha is positive and imaginary part of beta is negative, then the complex number (alpha+beta)//(alpha-beta) may be

If (a+b+c)>0 and a < 0 < b < c, then the equation a(x-b)(x-c)+b(x-c)(x-a)+c(x-a)(x-c)=0 has (i) roots are real and distinct (ii) roots are imaginary (iii) product of roots are negative (iv) product of roots are positive

If a complex number Z is purely imaginary then conjugate of Z is

If a complex number Z is purely imaginary then conjugate of Z is