Question

If α, β are the roots of 7x² + ax + 2 = 0 and if β – α = `(-13)/7` Find the values of a

Answer 1

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