Question

consider the quadratic equation x^2+x+1=0 solve the quadratic equation​

Answer 1

Answer:

$x {}^{2} + x + 1 = 0 \\ x(x + 1) + 1(x + 1) = 0 \\ (x + 1)(x + 1) = 0 \\ (x + 1) \: {}^{2} = 0$

Answer 2

Answer:x2+x+1=0

By completing square method,

term to be added=(coefficient of x X 1/2)2

(1 X1/2)2

(1/2)2

1/4

x2+x+1 +1/4 - 1/4=0

x2+x+1/4=-1+1/4

(x+1/2)2= 1+4/4

(x+1/2)2=5/4

by taking square root both the sides,

x+1/2 = + √5/2          or            x+1/2 = -√5/2    

x=-1/2  + √5/2           or            x= -1/2-√5/2    

x=-1 +√5/2                  or             x =  -1-√5/2