How do you know if a polynomial of degree 2 has an x-intercept?
Once you have it in standard
Any polynomial of degree
This has discriminant
#Delta = b^2-4ac#
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