If $p,q$ be non-zero real numbers and $f\left(x\right)\neq 0$ in $\left[0,2\right]$ and ${\int}_{0}^{1}f\left(x\right).\left(x^{2}+px+q\right)dx={\int}_{0}^{2}f\left(x\right).\left(x^{2}+px+q\right)dx=0$ then equation $x^{2}+px+q=0$ has