Let and be real and be a complex number

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Let α\alpha and β\beta be real and zz be a complex number. If z2+αz+β=0z^2 + \alpha z + \beta = 0 has two distinct roots on the line Re(z)=1\text{Re}(z) = 1, then it is necessary that (1) β∈(−1,0)\beta \in (-1, 0) (2) ∣β∣=1|\beta| = 1 (3) β∈(1,∞)\beta \in (1, \infty) (4) β∈(0,1)\beta \in (0, 1)

Related theory

Browse the problem library