Use the discriminant to describe the roots of each equation. then select the best description. 6x2 + 13x + 6 = 0
double root
real and rational roots
real and irrational roots
non-real roots

The quadratic formula for a quadratic of the form ax^2+bx+c is

x=(-b±)/(4a)

The discriminant is the part under the radical sign.

There are three possibilities for the discriminant and the roots that the formula will produce.

The discriminant is positive:  There will be two real roots.

The discriminant is negative:  There will be no REAL root, however there will be two imaginary roots

The discriminant is zero.  There will be one real root.

In this example.  b^2-4ac=169-144=25

So there will be two real roots as it is greater than zero.