as you know for every set of orthogonal polynomials as $P_0(x)=1, P_1(x), P_2(x),..., P_n(x), ...$ we have exactly $n$ real roots for $P_n(x)$ and also the fact that $\int_a^b P_i(x)P_j(x)d\alpha(x)=0$ where $(a,b)$ is the interval of orthogonality .
let $a=-1,b=1$ and $\alpha(x)=x$ and all $P_n(x)$ be monic polynomials, now let us modify our set of orthogonal polynomial a little more, let $\int_{-1}^1 P_i(x)P_j(x)dx=\frac{1}{2}$ for every different $i,j$ ,then using this calculator we will have the following polynomials :
with the set of following roots :
and they are really similar to the orthogonal polynomials $\int_{-1}^1 P_i(x)P_j(x)dx=0$, I mean they both have the same number of different roots where they separate each other, but our modified verison also contains some complex roots that are yet still different and also may have a root outside the boundery, and this is even true when you use other constant but not just $\frac{1}{2}$ !
I wish to know is there any related fact between these polynomials and orthogonal polynomials? do they have a name? or no, it's just some exceptions that we are dealing with?