What are the roots of the quadratic equation below?

x 2 + 2x = - 5

To find the roots of the quadratic equation x^2 + 2x + 5 = 0 is the same as solving it for x.

The formula to get x₁ and x₂ is: x₁, x₂ = (-b⁺/₋√ (b²-4ac)) / (2a) where in our case a=1, b=2 and c=5.

Lets input the numbers:

x₁, x₂ = (-2⁺/₋√ (2²-4*1*5)) / (2*1) = (-2⁺/₋√ (4-20)) / 2, = (-2⁺/₋√ (-16)) / 2

We see that we have a minus sign under the square root so the solutions or roots for our quadratic equation are going to be complex numbers:

x₁ = (-2+4i) / 2 = - 1+2i

x₂ = (-2-4i) / 2 = - 1-2i

So our roots are complex and are: x₁ = - 1+2i and x₂ = - 1-2i.

This is the concept of quadratic equations, to get the root of quadratic equation given we proceed as follows;

x^2+2x=-5

Writing the above in the quadratic form ax^2+bx+c=0 we get;

x^2+2x+5=0

(x+1) ^2+4=0

x=-1-2i

x=-1+2i

where i=√-1