Question

Find the roots of the following equation, if they exist, by applying the quadratic formula:

x² + x + 2 = 0

Answer 1

Given: x² + x + 2 = 0

Step-wise calculation:

1. Compare with ax² + bx + c = 0:

a = 1, b = 1, c = 2

2. Quadratic formula:

`x = (-b ± sqrt(b^2 - 4ac))/(2a)`

3. Compute discriminant:

D = b² – 4ac

= 1² – 4(1)(2) 

= 1 – 8

= –7

4. Substitute:

`x = (-1 ± sqrt(-7))/2` 

= `(-1 ± isqrt(7))/2`

The equation has no real roots; its two complex conjugate roots are `x = (-1 + isqrt(7))/2` and `x = (-1 - isqrt(7))/2`.