Question 953145
{{{3x^2-7x+k=0}}}

discriminant is {{{b^2-4ac}}}

if and only if  {{{b^2-4ac<0}}} we have two imaginary solutions

in your case {{{a=3}}},{{{b=-7}}}, and {{{c=k}}}

so, {{{(-7)^2-4*3k<0}}}
=>{{{49-12k<0}}}
=>{{{49<12k}}}
=>{{{49/12<k}}}
=>{{{4.083333333333333<k}}}
=>{{{k>4.08}}}

the smallest integer (whole number) value is {{{k=5}}} that makes the solutions of {{{3x^2-7x+k=0}}} imaginary