Let , be real and z be a complex number. If z^2+ z+ =0 has two distinct roots on the line Re z=1 , then it is necessary that

Step-by-step solution

Suppose roots are 1+ pi , 1+ qi Sum of roots 1+p i+1+q i=- which is real roots of 1+ pi , 1- pi Product of roots = =1+p^2 (1, ) p 0 since roots are distinct.