Question 298071
The discriminant is the quantity inside the radical of the quadratic formula.  This is {{{b^2 - 4ac}}}.  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, {{{x^2 +4x+3=0}}}, the discriminant is {{{4^2 -4*1*3}}}, which is {{{16-12=4}}}.  Since this is positive, there are TWO real roots.


Dr. Robert J. Rapalje, Retired
Seminole State College of Florida