Question 1127899
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To satisfy the problem's requirement, the discriminant of the equation must be non-negative:


{{{b^2 - 4ac}}} >= 0,


{{{b^2 - 4*(-3)*(-1)}}} >= 0,


{{{b^2 - 12}}} >= 0,


{{{b^2}}} >= 12  ====>   b >= {{{sqrt(12)}}} = {{{2*sqrt(3)}}}   OR   b <= -{{{sqrt(12)}}} = {{{-2*sqrt(3)}}}.


<U>Answer</U>.  The necessary and sufficient condition for "b"  is  |b| >= {{{2*sqrt(3)}}} =~ 3.464102 .
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Solved.