Let p, q, r ∈ R and r p 0. If the quadratic equation px2 + qx + r = 0 has two complex roots α and β, then |α|+|β| is

Question

Let p, q, r ∈ R and r > p > 0. If the quadratic equation px2 + qx + r = 0 has two complex roots α and β, then |α|+|β| is (A) equal to 1 (B) less than 2 but not equal to 1 (C) greater than 2 (D) equal to 2

Tardigrade Admin · Accepted Answer

Given quadratic equation is px2+qcx+r=0 ...(1) D=q2-4pr Since α and β are two complex root ∴ β= barα ⇒ |β|=| barα| ⇒ |β|=|α| (∵ | barα|=|α|) Consider |α|+|β|=|α|+|α| (∵|β|=|α|) =2|α| > 2.1=2 (∵ | barα |> 1) Hence, |α |+|β | is greater than 2.

Q. Let p,q,r∈R and r>p>0. If the quadratic equation px2+qx+r=0 has two complex roots α and β, then ∣α∣+∣β∣ is

equal to 1

less than 2 but not equal to 1

greater than 2

equal to 2

Q. Let $p, q, r \in R$ and $r > p > 0$ . If the quadratic equation $p x^{2} + q x + r = 0$ has two complex roots $α$ and $β$ , then $∣ α ∣ + ∣ β ∣$ is