The condition that the equation `az^2 + bz + c = 0` hasboth purely imaginary roots where `a, b, c` are non-zero complex constants, is

If roots of the equation z^(2)+az+b=0 are purely imaginary then

If a,b,c are non-zero real numbers and the equation ax^(2)+bx+c+i=0 has purely imaginary roots,then

Consider a quadratic equation az^2 + bz + c =0 where a, b, c, are complex numbers. Find the condition that the equation has (i) one purely imaginary root (ii) one purely real root (iii) two purely imaginary roots (iv) two purely real roots

If coefficients of the equation ax^(2)+bx+c=0,a!=0 are real and roots of the equation are non-real complex and a+c

If a,b,c are nonzero real numbers and az^(2)+bz+c+i=0 has purely imaginary roots,then prove that a=b^(2)c.

If the cubic equation z^(3)+az^(2)+bz+c=0 AA a, b, c in R, c ne0 has a purely imaginary root, then (where i^(2)=-1 )

The quadratic equation p(x)=0 with real coefficients has purely imaginary roots.Then the equation p(p(x))=0 has A.only purely imaginary roots B.all real roots C.two real and purely imaginary roots D.neither real nor purely imaginary roots

If a and b are complex and one of the roots of the equation x^(2) + ax + b =0 is purely real whereas the other is purely imaginary, then

If a and b are complex and one of the roots of the equation x^(2) + ax + b =0 is purely real whereas the other is purely imaginary, then