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4-1.Complex numbers
medium
Solve the equation $x^{2}+3 x+5=0$
A
$\frac{-3 \pm \sqrt{11} i}{2} $
B
$\frac{-3 \pm \sqrt{11} i}{2} $
C
$\frac{-3 \pm \sqrt{11} i}{2} $
D
$\frac{-3 \pm \sqrt{11} i}{2} $
Solution
The given quadratic equation is $x^{2}+3 x+5=0$
On comparing the given equation with $a x^{2}+b x+c=0$
We obtain $a=1, b=3,$ and $c=5$
Therefore, the discriminant of the given equation is
$D=b^{2}-4 a c=3^{2}-4 \times 1 \times 5=9-20=-11$
Therefore, the required solutions are
$\frac{-b \pm \sqrt{D}}{2 a}=\frac{-3 \pm \sqrt{-11}}{2 \times 1}=\frac{-3 \pm \sqrt{11} i}{2} \quad[\sqrt{-1}=i]$
Standard 11
Mathematics
