If the roots of the quadratic equation x 2 + p x + q = 0 are tan 3 0 ∘ and tan 1 5 ∘ , respectively then the value of 2 + q − p is

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x 2 + p x + q = 0 tan 3 0 ∘ + tan 1 5 ∘ = − p tan 3 0 ∘ ⋅ tan 1 5 ∘ = q tan 4 5 ∘ = 1 − t a n 3 0 ∘ t a n 1 5 ∘ t a n 3 0 ∘ + t a n 1 5 ∘ ​ = 1 − q − p ​ = 1 ⇒ − p = 1 − q ⇒ q − p = 1 ∴ 2 + q − p = 3 .

Mathematics - Quadratic Equation Question with Solution | TestHub

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