If α, β ∈ R are such that 1-2 i (here . i 2=-1) is a root of z2+α z+β=0, then (α-β) is equal to :

Question

If α, β ∈ R are such that 1-2 i (here . i 2=-1) is a root of z2+α z+β=0, then (α-β) is equal to : (A) -3 (B) -7 (C) 7 (D) 3

Tardigrade Admin · Accepted Answer

∵ α, β ∈ R ⇒ other root is 1+2 i α=-( sum of roots )=-(1-2 i +1+2 i )=-2 β= product of roots =(1-2 i )(1+2 i )=5 ∴ α-β=-7

Q. If $α, β \in R$ are such that $1 - 2 i$ (here $i^{2} = - 1)$ is a root of $z^{2} + α z + β = 0,$ then $(α - β)$ is equal to :