Question 870790
Just by graphing?  Use general solution of the quadratic equation to find the roots and then draw the graph.  If computing the discriminant gives a negative number, then no real roots can be shown.


{{{8^2-4*1*14=64-4*14=64-56=8}}}


The x-intercepts will be two irrational values.

zeros or roots are {{{(-8-sqrt(8))/2}}} and {{{(-8+sqrt(8))/2}}};
or {{{-4-sqrt(2)}}} and {{{-4+sqrt(2))}}}.  Those are exact irrational real roots.


{{{graph(200,200,-6,1,-4,3,x^2+8x+14)}}}