$q(x)=x\,x-a\,x$

$q(x)=0 \implies (x=0\lor x=a)$

$p(x)=x\,x-a\,x+b$

$p(x)=0 \implies x=a\cdot\dfrac{1+\epsilon\sqrt{1-\left(\frac{2}{a}\right)^2\cdot b}}{2}, \epsilon=\pm 1$

$\lim_{b\to 0}\sqrt{1-\left(\frac{2}{a}\right)^2\cdot b}=1$

Series[(1 + \[Epsilon] Sqrt[1 - d])/2, {d, 0, 5}]

Wikipedia:

Analytic function

Complex number