# How do you know if a polynomial of degree 2 has an x-intercept?

##### 1 Answer

Mar 6, 2016

Once you have it in standard

#### Explanation:

Any polynomial of degree

#ax^2+bx+c#

This has discriminant

#Delta = b^2-4ac#

If

Roots of

The roots of

#x = (-b+-sqrt(b^2-4ac))/(2a) = (-b+-sqrt(Delta))/(2a)#

Notice that the discriminant is the expression under the square root, so the square root takes Real values if and only if