Correct Answer - Option 2 : x

^{2} + 8x + 16 = 0

**Calculation:**

α, β are the roots of x2 - 2x + 2 = 0

Then, α + β = 2 , αβ = 2

⇒ (α + β)^{2} = 2^{2}

⇒ α^{2} + β^{2} + 2αβ = 4

⇒ α2 + β2 = 4 - 4 = 0

⇒ (α2 + β2 )^{2} = 0

⇒ α^{4} + β^{4} + 2α2β2 = 0

⇒ α4 + β4 = - 8

⇒ α^{4}β^{4} = 2^{4} = 16

The equation whose roots are α4, β^{4}

⇒ x^{2} - (α4 + β4 )x + α4β^{4} = 0

⇒ x^{2} + 8x + 16 = 0

**∴ The equation whose roots are α4, β**^{4} is x2 + 8x + 16 = 0.