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.
 

Updated on: 10-Oct-2022

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