Question

If α and β are the roots of the quadratic equation x2 + x + 1 = 0, then the equation whose roots are α2000, β2000 is

Answer 1

From the given,
α + β = 1 .
α β = 1 .

α =1/ β

α + β = 1

1 / β + β = 1

β²+1 = β

β²-β+1= 0

β = 1 ± √ 1 - 4 ( 1 ) (1 ) / 2 = 1±√-3 / 2 = 1 ± √3i/ 2 .

Now, product of roots = α^2000 β^2000 = α^2000 *1/ α^2000 = 1 .

Sum of roots = .