The teacher will be very surprised to see your correct solution 😉
a*x^2 + b*x + c = 0
D = b^2 - 4 * a * c =
(-1)^2 - 4 * (1) * (1) = -3
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
sum
___ ___ 1 I*\/ 3 1 I*\/ 3 - - ------- + - + ------- 2 2 2 2
=
1
product
/ ___\ / ___\ |1 I*\/ 3 | |1 I*\/ 3 | |- - -------|*|- + -------| \2 2 / \2 2 /
=
1
1
___ 1 I*\/ 3 x1 = - - ------- 2 2
___ 1 I*\/ 3 x2 = - + ------- 2 2
x2 = 1/2 + sqrt(3)*i/2
x1 = 0.5 + 0.866025403784439*i
x2 = 0.5 - 0.866025403784439*i
x2 = 0.5 - 0.866025403784439*i