# What are the zero(s) of x^2 + 2x + 10 = 0?

Nov 3, 2015

There are no real solutions.

#### Explanation:

To solve a quadratic equation $a {x}^{2} + b x + c = 0$, the solving formula is

${x}_{1 , 2} = \setminus \frac{- b \setminus \pm \setminus \sqrt{{b}^{2} - 4 a c}}{2 a}$

In your case, $a = 1$, $b = 2$ and $c = 10$. Plug these values into the formula:

${x}_{1 , 2} = \setminus \frac{- 2 \setminus \pm \setminus \sqrt{{\left(- 2\right)}^{2} - 4 \cdot 1 \cdot 10}}{2 \cdot 1}$

Doing some easy calculations, we get

${x}_{1 , 2} = \setminus \frac{- 2 \setminus \pm \setminus \sqrt{4 - 40}}{2}$

and finally

${x}_{1 , 2} = \setminus \frac{- 2 \setminus \pm \setminus \sqrt{- 36}}{2}$

As you can see, we should compute the square root of a negative number, which is a forbidden operation if using real numbers. So, in the real number set, this equation has non solutions.