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 = 22
⇒ α2 + β2 + 2αβ = 4
⇒ α2 + β2 = 4 - 4 = 0
⇒ (α2 + β2 )2 = 0
⇒ α4 + β4 + 2α2β2 = 0
⇒ α4 + β4 = - 8
⇒ α4β4 = 24 = 16
The equation whose roots are α4, β4
⇒ x2 - (α4 + β4 )x + α4β4 = 0
⇒ x2 + 8x + 16 = 0
∴ The equation whose roots are α4, β4 is x2 + 8x + 16 = 0.