quadratic algebra

A non-associative algebra $A$ (with unity $1_A$) over a commutativering $R$ (with unity $1_R$) is called a quadratic algebra if$A$ admits a quadratic form $Q:A\to R$ such that

1. $Q(1_A)=1_R$,

2. the quadratic equation $x^2-b(1_A,x)x+Q(x)1_A=0$ is satisfiedby all $x\in A$, where $b$ is the associated symmetric bilinear formgiven by $b(x,y):=Q(x+y)-Q(x)-Q(y)$.