Question 1098764
The quadratic function would be greater than zero for all x.  This means the discriminant must be negative.  That should help you.


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{{{2x^2+bx+5>0}}}


Discriminant is  {{{b^2-4*2*5}}},
{{{b^2-40}}}.


The function {{{2x^2+bx+5}}} is a parabola having a minimum vertex and the parabola opens upward.    If {{{b^2-40>0}}}, then the parabola will cross the x-axis in two places and there will be some points below the x-axis.  If {{{b^2-40<0}}}, then the parabola will not touch nor cross the x-axis anywhere, and all points of the parabola will be greater than 0  (or all points will be above the x-axis).