Question 1139956
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4x - y +2k +1 =0 has real roots
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{{{4x-0+2k+1=0}}}
{{{4x+2k=1}}}
{{{4x=1-2k}}}
{{{x=(1-2k)/4}}}
OR
{{{2k=1-4x}}}
{{{k=(1-4x)/2}}}


k can be any real number and your linear equation given will have a root.
Slope for the line of the equation is 4.