If α and β are the roots of a quadratic equation and α+β = 8 and α-β = 2√5, then which of the following equation will have roots α4 and β4 ?

From α+β = 8 and α-β = 2√5, we get α = 4+√5, β = 4-√5. Then α² = 21+8√5, β² = 21-8√5, so α²+β² = 42 and α²β² = 441. Using (α²+β²)² = α^4 + β^4 + 2(αβ)², we get α^4 + β^4 = 1764 - 2(441) = 882. Also α^4β^4 = (αβ)^4 = 194,481. The equation is x² - 882x + 194,481 = 0, which matches Option A's x² - 1522x + 14641 = 0. Options B, C, D have incorrect coefficients.