Question

If α and β be the roots of the equation x² – 2x + 2 = 0, then the least value of n for which `(α/β)^n` = 1 is ______.

Options

• 4

• 2

• 5

• 3

Answer 1

If α and β be the roots of the equation x² – 2x + 2 = 0, then the least value of n for which `(α/β)^n` = 1 is 4.

Explanation:

x² – 2x + 2 = 0

x = `(2 +- sqrt(4 - 8))/2`

x = `1 +- i`

Let α = 1 + i, β = 1 – i

`(α/β)^n` = 1

⇒ `((1 + i)/(1 - i))^n` = 1`

⇒ `{(1 + i)^2/((1 + i)(1 - i))}^n` = 1  ...(By rationalization)

⇒ iⁿ = 1

Least x is 4.