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

1 Answer
KillerBunny
Nov 3, 2015

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.

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