If `a ,b ,c` are nonzero real numbers and `a z^2+b z+c+i=0` has purely imaginary roots, then prove that `a=b^2c dot`

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

if ax^(2)+bx+c=0 has imaginary roots and a+c

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

If ax^(2)+bx+c=0 has imaginary roots and a,b,c in Rsuch that a+4c<2b then

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 )

Let a ,b ,a n dc be any three nonzero complex number. If |z|=1a n d' z ' satisfies the equation a z^2+b z+c=0, prove that a a =c c a n d|a||b|=sqrt(a c( b )^2)

If a, b and c are positive real and a = 2b + 3c , then the equation ax^(2) + bx + c = 0 has real roots for

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 one root of ax^(2)+bx-2c=0(a,b,c real) is imaginary and 8a+2b>c, then