Question

If α and β are the roots of the equation x² + 2x + 4 = 0, then `1/α^3 + 1/β^3` is equal to ______.

Options

• `-1/2`

• `1/2`

• 32

• `1/4`

Answer 1

If α and β are the roots of the equation x² + 2x + 4 = 0, then `1/α^3 + 1/β^3` is equal to `underlinebb(1/4)`.

Explanation:

Given equation is x² + 2x + 4 = 0

Since α, β are roots of this equation

∴ α + β = –2 and αβ = 4

Now, `1/a^3 + 1/β^3 = (α^3 + β^3)/(αβ)^3` 

= `((α + β)(α^2 + β^2 - αβ))/(αβ)^3`

= `((-2)((α + β)^2 - 3αβ))/(4 xx 4 xx 4)`

= `(-2(4 - 12))/(4 xx 4 xx 4)`

= `1/4`