You can put this solution on YOUR website!
List of factors of the constant term 2.
Factors of 2: ±1, ±2
List the factors of the leading coefficient 3.
Factors of 3: ±1, ±3
List all the POSSIBLE rational zeros or roots.
This list comes from taking all the factors of the constant and writing them over all the factors of the leading coefficient.
Rational zeros or roots:
±1/1, ±1/3, ±2/1, ±2/3
NOTE: ±1/1 becomes ±1 and ±2/1 becomes ±2 because they are both over 1 in fraction form.
Use synthetic division to test the possible zeros and find an actual zero.
Then replace your zero(s) with α^2+ß^2 and square both to find your sum.
Can you take it from here?