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

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 ax^2+bx+c = 0 has imaginary roots and a+c lt b then prove that 4a+c lt 2b

if ax^2+bx+c = 0 has imaginary roots and a+c lt b then prove that 4a+c lt 2b

if ax^2+bx+c = 0 has imaginary roots and a+c lt b then prove that 4a+c lt 2b

If a and c are odd prime numbers and a x^2+b x+c=0 has rational roots , where b in I , prove that one root of the equation will be independent of a ,b ,c dot

If a ,b ,c are nonzero complex numbers of equal moduli and satisfy a z^2+b z+c=0, hen prove that (sqrt(5)-1)//2lt=|z|lt=(sqrt(5)+1)//2.

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