Question 1051694
4 x squared plus 5 x plus 1 equals 04x2+5x+1=0
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{{{4x^2+5x+1=0}}}



{{{ax^2+bx+c=0}}}
Discriminant is {{{b^2-4ac}}}.


Not just the sign you are using to decide.  Also the rationality or irrationality is part of your determination.



YOU can do this.
{{{sqrt(b^2-4ac)}}} positive WHOLE number, then two Real RATIONAL solutions.
{{{b^2-4ac<0}}} means nonreal complex solutions, two of them.
{{{sqrt(b^2-4ac)>0}}} but irrational, then two irrational solutions.


FORM your discriminant!