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For what values of $k$, the roots of the equation $x^{2}+4x+k=0$ are real?
Given: Equation $x^{2}+4x+k=0$
To do: To find the value of k for which given equation have equal roots.
Solution:
Given Equation $x^{2}+4x+k=0$
By comparing it to standard equation $ax^{2}+bx+c=0$
$a=1,\ b=4$ and $c=k$
Its discriminant $D=b^{2}-4ac$
$=4^{2}-4×1×k$
$=16-4k$
for real roots $D≥0$
$\Rightarrow 16-4k≥0$
$\Rightarrow 4k≤16$
$\Rightarrow k≤\frac{16}{4}$
$\Rightarrow k≤4$
For $k≤4$, the given quadratic equation will have real roots.
 
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