How do you solve #x^2 - x + 2 = 0#?

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Answer 1 · 2015-10-10T06:22:53

The solutions are
#color(blue)(x= (1+sqrt(-7))/2#

#color(blue)(x= (1-sqrt(-7))/2#

#x^2-x+2#

The equation is of the form #color(blue)(ax^2+bx+c=0# where:
#a=1, b=-1, c=2#

The Discriminant is given by:
#Delta=b^2-4*a*c#
# = (-1)^2-(4*1*2)#
# = 1-8=-7#

The solutions are found using the formula
#x=(-b+-sqrtDelta)/(2*a)#

#x = (-(-1)+-sqrt(-7))/(2*1) = (1+-sqrt(-7))/2#

The solutions are
#color(blue)(x= (1+sqrt(-7))/2#
#color(blue)(x= (1-sqrt(-7))/2#