You can put this solution on YOUR website!
The discriminant is the quantity inside the radical of the quadratic formula. This is
. It turns out that if the discriminant is positive, then there will be two real roots; if the discriminant is 0, then there will be one (double!) real root; and if the discriminant is negative, there will be NO real roots--in other words the roots will be complex.
In your example,
, the discriminant is
, which is
. Since this is positive, there are TWO real roots.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida