Question

If α and β are the roots of the equation 2x² – 3x – 6 = 0. The equation whose roots are `1/α` and `1/β` is:

विकल्प

• 6x² – 3x + 2 = 0

• 6x² + 3x – 2 = 0

• 6x² – 3x – 2 = 0

• x² + 3x – 2 = 0

Answer 1

6x² + 3x – 2 = 0

Explanation:

Here a = 2, b = –3, c = –6

α + β = `(-"b")/"a" = 3/2` and αβ = `"c"/"a" = (-6)/2` = –3

∴ s = `1/α + 1/β = (β + α)/(αβ) = (3/2)/(-3) = (-1)/2`

p = `1/α xx 1/β = 1/(αβ) = 1/-3`

The equation is x² – s(x) + p = 0

⇒ `"x"^2 - ((-1)/2) "x" + (1/(-3))`

∴ 6x² + 3x – 2 = 0