Question

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

(a) β ∈ (-1, 0)

(b) |β| = 1

(c) β ∈ [1, ∞)

(d) β ∈ (0, 1)

Answer 1

Correct option (c) β ∈ [1, ∞)

Explanation:

Since, the complex roots are conjugate of each other.