We have , x2+

x

√2

+ 1 = 0
Comparing the given equation with the general form ax2 + bx + c = 0,
we get a = 1 , b =

1

√2

, c = 1
∴ x =

−b±√b2−4ac

2a

=

− 1 √2 ±√( 1 √2 )2−4×1×1

2.1

=

− 1 √2 +√ 1 2 −4

2

=

− 1 2 ±√ 1−8 2

2

=

− 1 √2 ±√− 7 2

2

=

−1±i√7

2√2

∴ The roots of the given equation are

−1+i√7

2√2

and

−1−i√7

2√2