Question #0e722

1 Answer
Dec 14, 2017

x = {(1- sqrt(7)i)/2, (1+ sqrt(7)i)/2}

Explanation:

x^2-x+1=-1

=>x^2-x+2=0

Using,

For, ax^2+bx+c=0

x = (-b+- sqrt(b^2-4ac))/(2a)

Here, a=1, b=-1 and c=2.

x = (-(-1)+- sqrt((-1)^2-4(1)(2)))/(2(1))

x = (1+- sqrt(1-8))/2

x = (1+- sqrt(7)i)/2; where i = sqrt(-1)

So, we can see that both the roots of this equation are imaginary numbers.