Question

Solve following equation:

$-x^2+x-2=0$

• A. $\frac{\left(1\pm \sqrt{7}i\right)}{2}$
• B. $\frac{\left(-1\pm \sqrt{7}i\right)}{2}$
• C. $\frac{\left(2\pm \sqrt{7}i\right)}{2}$
• D. $\frac{\left(-2\pm \sqrt{7}i\right)}{2}$

Answer 1

The correct option is A

$\frac{\left(1\pm \sqrt{7}i\right)}{2}$

Given: $-x^2+x-2=0$

We know that the general form of quadratic equation is $a{x}^2+bx+c=0$

Comparing the given equation with the general form of the quadratic equation , we get;

$a=-1,b=1andc=-2$

Now, using quadratic formula, $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

So,

$$\begin{gathered} x=\frac{-1\pm \sqrt{\left(1^2-4\times -1\times -2\right)}}{2\times -1} \\ =\frac{-1\pm \sqrt{1-8}}{-2} \\ =\frac{-1\pm \sqrt{-7}}{-2} \\ =\frac{1\pm \sqrt{7}i}{2} \end{gathered}$$

Hence, the value of $x=\frac{1\pm \sqrt{7}i}{2}$