Question 985667
<pre>
That will be when the discriminant is positive:

bē-4ac = bē-4(6)(11) > 0
              bē-264 > 0
                  bē > 264
              
Taking positive square roots:

                   b > 16.24807681

Smallest positive integer is the next higher positive integer, b=17.

When b=16, no x-intercepts:

{{{graph(200,200,-3,3,-2,4,6x^2+16x+11)}}}

When b=16.24807681, 1 x-intercept:

{{{graph(200,200,-3,3,-2,4,6x^2+sqrt(264)x+11)}}}

When b=17, 2 x-intercepts:

{{{graph(200,200,-3,3,-2,4,6x^2+17x+11)}}}

Edwin</pre>