Let α,β be real and z be a complex number. If z² + α z + β = 0 has two distinct roots on the line Re z = 1, then it is necessary that:

Complex Numbers and Quadratic Equations: JEE Main 2011 Mathematics question

JEE Main 2011 · Annual, Paper 1 · Q3175

JEE Main 2011Annual, Paper 1MathematicsEasyComplex Numbers and Quadratic Equations264× since 2002

Let

\alpha \,,\beta

be real and z be a complex number. If

{z^2} + \alpha z + \beta = 0

has two distinct roots on the line Re z = 1, then it is necessary that :

JEE Main 2011 · Annual, Paper 1 · Q3175

JEE Main 2011Annual, Paper 1MathematicsEasyComplex Numbers and Quadratic Equations264× since 2002

Let

\alpha \,,\beta

be real and z be a complex number. If

{z^2} + \alpha z + \beta = 0

has two distinct roots on the line Re z = 1, then it is necessary that :