If α and β are roots of the equation x 2 + p x + 4 3 p = 0 , such that ∣ α − β ∣ = 10 , then p belongs to the set :

Question

If α and β are roots of the equation x 2 + p x + 4 3 p ​ = 0 , such that ∣ α − β ∣ = 10 ​ , then p belongs to the set :

TestHub · Accepted Answer

Given quadratic eqn. is x 2 + p x + 4 3 p ​ = 0 So, α + β = − p , α β = 4 3 p ​ Now, given ∣ α − β ∣ = 10 ​ ​ ⇒ α − β = ± 10 ​ ⇒ ( α − β ) 2 = 10 ⇒ α 2 + β 2 − 2 α β = 10 ⇒ ( α + β ) 2 − 4 α β = 10 ⇒ p 2 − 4 × 4 3 p ​ = 10 ⇒ p 2 − 3 p − 10 = 0 ⇒ p = − 2 , 5 ⇒ p ∈ { − 2 , 5 } ​

Mathematics - Quadratic Equation Question with Solution | TestHub

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