The teacher will be very surprised to see your correct solution 😉
a*y^2 + b*y + c = 0
D = b^2 - 4 * a * c =
(0)^2 - 4 * (3) * (2*x^2) = -24*x^2
y1 = (-b + sqrt(D)) / (2*a)
y2 = (-b - sqrt(D)) / (2*a)
___ ___ \/ 6 *im(x) I*\/ 6 *re(x) y1 = ----------- - ------------- 3 3
___ ___ \/ 6 *im(x) I*\/ 6 *re(x) y2 = - ----------- + ------------- 3 3
y2 = sqrt(6)*i*re(x)/3 - sqrt(6)*im(x)/3
sum
___ ___ ___ ___ \/ 6 *im(x) I*\/ 6 *re(x) \/ 6 *im(x) I*\/ 6 *re(x) ----------- - ------------- + - ----------- + ------------- 3 3 3 3
=
0
product
/ ___ ___ \ / ___ ___ \ |\/ 6 *im(x) I*\/ 6 *re(x)| | \/ 6 *im(x) I*\/ 6 *re(x)| |----------- - -------------|*|- ----------- + -------------| \ 3 3 / \ 3 3 /
=
2 -2*(-im(x) + I*re(x)) ---------------------- 3
-2*(-im(x) + i*re(x))^2/3