Question

Find the values of g for which the function
y = 2x^2 − (3g − 1)x + (2g − 5) has:
(a) one zero equal to 0 (let the zeroes be 0 and α),
(b) the sum of the zeroes equal to their product (put α + β = αβ),
(c) the zeroes as reciprocals of one another (let the zeroes be α and 1/α),
(d) the zeroes equal in magnitude but opposite in sign (let the zeroes be α and −α).