Question

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

Answer 1

There are no real solutions.

Explanation:

To solve a quadratic equation `ax^2+bx+c=0`, the solving formula is

`x_{1,2} = \frac{-b\pm\sqrt(b^2-4ac)}{2a}`

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

`x_{1,2} = \frac{-2\pm\sqrt((-2)^2-4*1*10)}{2*1}`

Doing some easy calculations, we get

`x_{1,2} = \frac{-2\pm\sqrt(4-40)}{2}`

and finally

`x_{1,2} = \frac{-2\pm\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.