Question

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

Answer 1

Answer:

No real root.

Complex roots:

$x = -1 \pm 2i$

Step-by-step 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.

$x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

$x = \dfrac{-2 \pm \sqrt{2^2 - 4(1)(5)}}{2(1)}$

$x = \dfrac{-2 \pm \sqrt{4 - 20}}{2}$

$x = \dfrac{-2 \pm \sqrt{-16}}{2}$

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.

$x = \dfrac{-2 \pm 4i}{2}$

$x = -1 \pm 2i$

Answer 2

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.