Let p , q , r ∈ 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

Question

Let p , q , r ∈ 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

TestHub · Accepted Answer

Given quadratic equation is ​ p x 2 + q x + r = 0 D = q 2 − 4 p r ​ Since α and β are two complex root ∴ β = α ˉ ⇒ ∣ β ∣ = ∣ α ˉ ∣ ⇒ ∣ β ∣ = ∣ α ∣ ( ∵ ∣ α ˉ ∣ = ∣ α ∣ ) Consider ∣ α ∣ + ∣ β ∣ = ∣ α ∣ + ∣ α ∣ = 2∣ α ∣ > 2.1 = 2 ​ ( ∵ ∣ β ∣ = ∣ α ∣ ) ( ∵ ∣ α ∣ > 1 ) ​ Hence, ∣ α ∣ + ∣ β ∣ is greater than 2 .

Mathematics - Quadratic Equation Question with Solution | TestHub

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