​If α, β are roots of the equation x^2 + px – 1/2p^2 = 0,∀ p ∈ R– {0}, then the minimum value of α^4 + β^4 is ​

Question

If α, β are roots of the equation x² + px – \(\frac1{2p^2}\) = 0,∀ p ∈ R– {0}, then the minimum value of α⁴ + β⁴ is 

(a) 2√2

(b) 2 – √2

(c) 2

(d) 2 + √2

Answer 1

Correct option is (d) 2 + √2