There are so many identities related to alpha and beta .i.e zeroes and coefficients please tell me the identities which can come in exam and are very important ?

The most important one is that for a quadratic equation, ax^2 + bx+c = 0

sum of roots (alpha+beta) = -b/a

and product of roots (alpha*beta) = c/a. 

 

Most of the other identities for quadratic equation can derived from these 2 equations itself.