Question

Solve the equation $–x^2+x–2=0$

Answer 1

Step 1: Given, $–x^2+x–2=0$

Step 2: Check nature of roots
$D=b^2-4ac,a=–1,b=1,c=–2$
$\Rightarrow D=1-8=–7<0$
$\therefore D$ is negative
$\therefore$ Roots are imaginary, so we can use the quadratic formula .

Step 3:Using quadratic formula
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
By putting the values of $a,b,c$
$x=\frac{-1\pm (\sqrt{1-4(-1)(-2)}}{-2}=\frac{-1\pm \sqrt{-7}}{-2}=\frac{-1\pm \sqrt{7}i}{-2}(\because \sqrt{-1}=i)$.

The values of $x$ are $\frac{-1+\sqrt{7}i}{-2},\frac{-1-\sqrt{7}i}{-2}$