In this thesis we consider some polynomial identities of degree 5 which are satisfied by all symmetric quadratic algebras . Rings that satisfying these identities is called generalized quadratic rings , or GQ-rings . then we will consider flexible ring , and we will show that when the ring is not flexible , these identities are enough to make the ring quadratic over its center . Finally , we show that every semi prime QC-Ring is a subdirect sum of a noncom mutative Jordan ring and a non-flexible ring .