Find the least positive value of k for which the equation


Find the least positive value of $k$ for which the equation $x^{2}+k x+4=0$ has real roots.


The given quadric equation is $x^{2}+k x+4=0$, and roots are real.

Then find the value of $k$.


$a=1, b=k$ and,$c=4$

As we know that $D=b^{2}-4 a c$

Putting the value of $a=1, b=k$ and, $c=4$

$=(k)^{2}-4 \times 1 \times 4$


The given equation will have real and equal roots, if $D=0$


Now factorizing of the above equation




$=\pm 4$

Now according to question, the value of k is positive.

Therefore, the value of $k=4$


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