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Question
If α, β are the roots of 7x2 + ax + 2 = 0 and if β – α = `(-13)/7` Find the values of a
Solution
α and β are the roots of 7x2 + ax + 2 = 0
α + β = `-alpha/7`, αβ = `2/7`
Given β – α = `- 13/7`
⇒ α – β = `13/7`
Squaring on both sides
(α – β)2 = `(13/7)^2`
α2 + β2 = 2αβ = `169/49`
`(- "a"/7)^2 - 4(2/7) = 169/49`
⇒ `"a"^2/49 - 8/7 = 169/49`
`"a"^2/49 = 225/49`
⇒ `"a"^2 = (225 xx 49)/49`
a2 = 225
⇒ a = `± sqrt(225)` = ± 15
The value of a = 15 or – 15
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