diff --git a/include/boost/math/special_functions/detail/ibeta_inverse.hpp b/include/boost/math/special_functions/detail/ibeta_inverse.hpp
index b9f0995a6..90a94e644 100644
--- a/include/boost/math/special_functions/detail/ibeta_inverse.hpp
+++ b/include/boost/math/special_functions/detail/ibeta_inverse.hpp
@@ -631,8 +631,17 @@ T ibeta_inv_imp(T a, T b, T p, T q, const Policy& pol, T* py)
             // Try and compute the easy way first:
             //
             T bet = 0;
-            if(b < 2)
-               bet = boost::math::beta(a, b, pol);
+            if (b < 2)
+            {
+               try
+               {
+                  bet = boost::math::beta(a, b, pol);
+               }
+               catch (const std::overflow_error&)
+               {
+                  bet = tools::max_value<T>();
+               }
+            }
             if(bet != 0)
             {
                y = pow(b * q * bet, 1/b);
diff --git a/include/boost/math/tools/roots.hpp b/include/boost/math/tools/roots.hpp
index cb2c89123..ccf908f21 100644
--- a/include/boost/math/tools/roots.hpp
+++ b/include/boost/math/tools/roots.hpp
@@ -543,7 +543,15 @@ namespace detail {
          last_f0 = f0;
          delta2 = delta1;
          delta1 = delta;
-         detail::unpack_tuple(f(result), f0, f1, f2);
+         try
+         {
+            detail::unpack_tuple(f(result), f0, f1, f2);
+         }
+         catch (const std::overflow_error&)
+         {
+            f0 = max > 0 ? tools::max_value<T>() : -tools::min_value<T>();
+            f1 = f2 = 0;
+         }
          --count;
 
          BOOST_MATH_INSTRUMENT_VARIABLE(f0);