Find the roots of the following quadratic equation,if they exist,using the quadratic formula: $x^{2}+4x+5=0$.
(NONE) The given quadratic equation is $x^{2}+4x+5=0$.
Comparing this with the standard form $ax^{2}+bx+c=0$,we get $a=1$,$b=4$,and $c=5$.
The discriminant $D$ is given by $D = b^{2}-4ac$.
Substituting the values,$D = (4)^{2} - 4(1)(5) = 16 - 20 = -4$.
Since the discriminant $D < 0$,the square root of the discriminant $\sqrt{D}$ does not yield a real number.
Therefore,the given quadratic equation has no real roots.
Comparing this with the standard form $ax^{2}+bx+c=0$,we get $a=1$,$b=4$,and $c=5$.
The discriminant $D$ is given by $D = b^{2}-4ac$.
Substituting the values,$D = (4)^{2} - 4(1)(5) = 16 - 20 = -4$.
Since the discriminant $D < 0$,the square root of the discriminant $\sqrt{D}$ does not yield a real number.
Therefore,the given quadratic equation has no real roots.
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