We study the differential equation
−
(
p
(
x
)
y
′
)
′
+
q
(
x
)
y
′
=
λ
y
,
- (p(x) y’)’ + q(x) y’ = \lambda y,
where
p
(
x
)
p(x)
is a polynomial of degree at most 2 and
q
(
x
)
q(x)
is a polynomial of degree at most 1. This includes the classical Jacobi polynomials, Hermite polynomials, Legendre polynomials, Chebychev polynomials, and Laguerre polynomials. We provide a general electrostatic interpretation of zeros of such polynomials: a set of distinct, real numbers
{
x
1
,
…
,
x
n
}
\left \{x_1, \dots , x_n\right \}
satisfies
p
(
x
i
)
∑
k
=
1
k
≠
i
n
2
x
k
−
x
i
=
q
(
x
i
)
−
p
′
(
x
i
)
f
o
r
a
l
l
1
≤
i
≤
n
\begin{equation*} p(x_i) \sum _{k = 1 \atop k \neq i}^{n}{\frac {2}{x_k - x_i}} = q(x_i) - p’(x_i) \qquad \mathrm {for all}~ 1\leq i \leq n \end{equation*}
if and only if they are zeros of a polynomial solving the differential equation. We also derive a system of ODEs depending on
p
(
x
)
,
q
(
x
)
p(x),q(x)
whose solutions converge to the zeros of the orthogonal polynomial at an exponential rate.