Question #00865

1 Answer
Feb 12, 2017

Answer:

#x = -1/2 +- (sqrt(3)i)/2#

Explanation:

#x^2 + x + 1 = 0#

The discriminant, #D#, is

#D = ("coeff. of x")^2 - 4 xx "coeff. of x"^2 xx "constant"#

#D = 1^2 - 4 (1) (1)#

#D = 1 - 4#

#D = -3#

Solving for #x#; since #D# is negative, the equation has complex roots.

#x = (- "coeff. of x" +- (sqrt(D)))/(2* "coeff. of x"^2)#

#x = (-1 +- sqrt(-3))/(2*1)#

#x = (-1 +- sqrt(3)i)/2#

#x = -1/2 +- (sqrt(3)i)/2#