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Question Number 140973 by EnterUsername last updated on 14/May/21

If α and β are roots of the equation {2 x}^{2} + a x + b = 0,

then one of the roots of the equation 2 {(α x + β)}^{2} +

a (α x + β) + b = 0 is

(A) 0 (B) \frac{α + 2 b}{α^{2}}

(C) \frac{a α + b}{2 α^{2}} (D) \frac{a α - 2 b}{2 α^{2}}

Answered by TheSupreme last updated on 15/May/21

α = \frac{- a + \sqrt{Δ}}{4}

β = \frac{- a - \sqrt{Δ}}{4}

2 {(α x + β)}^{2} + a (α x + β) + b = 0

α x + β = α

x = \frac{α - β}{α}

α x + β = β

x = 0 (A)

Commented by EnterUsername last updated on 19/May/21

Thanks so much