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4-1.Complex numbers
medium
ઉકેલો : $x^{2}-x+2=0$
A
$\frac{1 \pm \sqrt{7} i}{2} $
B
$\frac{1 \pm \sqrt{7} i}{2} $
C
$\frac{1 \pm \sqrt{7} i}{2} $
D
$\frac{1 \pm \sqrt{7} i}{2} $
Solution
The given quadratic equation is $x^{2}-x+2=0$
On comparing the given equation with $a x^{2}+b x+c=0$
We obtain $a=1, b=-1,$ and $c=2$
Therefore, the discriminant of the given equation is
$D=b^{2}-4 a c=(-1)^{2}-4 \times 1 \times 2=1-8=-7$
Therefore, the required solutions are
$\frac{-b \pm \sqrt{D}}{2 a}=\frac{-(-1) \pm \sqrt{-7}}{2 \times 1}=\frac{1 \pm \sqrt{7} i}{2} \quad[\sqrt{-1}=i]$
Standard 11
Mathematics
