1 Answers
α + β = - 3 .......(1)
and αβ = \(\frac{-5}{2}\) .........(2)
(α - β)2 = (α + β)2 - 4αβ
= (-3)2 - 4 x \(\frac{-5}{2}\)
= 9 + 10
= 19
α - β = ±√19 ........(3)
By adding equations (1) and (3), we get
2α = - 3 ± √19
∴ α = \(\frac{- 3 ± \sqrt{19}}{2}\)
By subtracting equation (3) from (1), we get
2β = \(\frac{- 3\,\mp\,\sqrt{19}}{2}\)
⇒ β = \(\frac{- 3\,\mp\,\sqrt{19}}{2}\)
Hence,
Either α = \(\frac{- 3 + \sqrt{19}}{2}\) , β = \(\frac{- 3 - \sqrt{19}}{2}\)
Or, α = \(\frac{- 3 - \sqrt{19}}{2}\), β = \(\frac{- 3 + \sqrt{19}}{2}\)
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