How you can tell that the quadratic function #y=x^2 +6x+15# has no real zeroes without graphing the function?
When given a quadratic equation in standard form:
Check the value of the determinant:
If it is greater than zero, the equation will have two real roots.
If it is equal to zero, the equation will have one root (a.k.a. a repeated root).
If it is less than zero, the equation will have complex conjugate pair of roots.
In the case of the given equation
This equation will have a complex conjugate pair of roots