We use Turán type inequalities to give new non-asymptotic bounds on the extreme
zeros of orthogonal polynomials in terms of the
coefficients of their three term recurrence.
Most of our results deal with symmetric polynomials satisfying
the three term recurrence $p_{k+1}=x p_k-c_k p_{k-1},$
with a nondecreasing sequence $\{c_k\}$. As a special case
they include a non-asymptotic version of Máté, Nevai and Totik
result on the largest zeros of orthogonal polynomials with
$c_k=c \; k^{2 \delta} (1+ o(k^{-2/3})).$ Our proof is based on new Turán inequalities
which are obtained by analogy with higher order Laguerre inequalities.