Solve equation -x^{2}+x-2=0

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4-1.Complex numbers

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Solve the equation $-x^{2}+x-2=0$

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

$\frac{-b \pm \sqrt{D}}{2 a}=\frac{-1 \pm \sqrt{-7}}{2(-1)}=\frac{-1 \pm \sqrt{7} i}{-2} \quad[\sqrt{-1}=i]$

Standard 11

Mathematics

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