If `a ,b` are complex numbers and one of the roots of the equation `x^2+a x+b=0` is purely real, whereas the other is purely imaginary, prove that `a^2- a^-2=4b`.

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 , b are complex numbers and one of the roots of the equation x^(2)+ax+b=0 is purely real whereas the other is purely imaginery, and a^(2)-bara^(2)=kb , then k is

" The number of imaginary roots of the equation x^(2)+7x+2=0

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

If a,b,c are positive real numbers.then the number of real roots of the equation ax^(2)+b|x|+c=0 is

If a,b,c are positive real numbers,then the number of real roots of the equation ax^(2)+b|x|+c is

If the roots of the equation (b-c)x^(2)+(c-a)x+(a-b)=0 are equal,then prove that 2b=a+c

If a,b are real, then the roots of the quadratic equation (a-b)x^(2)-5 (a+b) x-2(a-b) =0 are