Question

What are the roots of the quadratic equation below?
x2 + 2x= -5

Answer 1

Answer: -1 +/- 2i (read -1 plus or minus 2i).

Using the quadratic formula given that a=1, b=2, c=5, the roots are:
(-2 +/- sqrt(4-4(1)(5)))/(2*1)= (-2 +/- sqrt(-16))/2= (-2 +/- 4i)/2.

Answer 2

No real root.

Complex roots:

`x = -1 \pm 2i`

Explanation:

`x^2 + 2x = -5`

`x^2 + 2x + 5 = 0`

There are no two integers whose product is 5 and whose sum is 2, so this trinomial is not factorable. We can use the quadratic formula.

`x = (-b \pm √(b^2 - 4ac))/(2a)`

`x = (-2 \pm √(2^2 - 4(1)(5)))/(2(1))`

`x = (-2 \pm √(4 - 20))/(2)`

`x = (-2 \pm √(-16))/(2)`

Since we have a square root of a negative number, there are no real roots. If you have learned complex numbers, then we can continue.

`x = (-2 \pm 4i)/(2)`

`x = -1 \pm 2i`