Question

What is the relationship between the discriminant solution and the types of roots?

Answer 1

The standard form of a quadratic equation is: \[\Large ax ^{2} + bx + c = 0\]The Discriminant D is defined as: \[\Large D = b ^{2} - 4ac\]Before finding the roots of the quadratic equation, we can tell a few things about the roots based on the discriminant D:

If D > 0, the quadratic equation will have two real roots
If D = 0, the quadratic equation will have two equal roots
If D < 0, the quadratic equation will have two complex roots

There are two additional things we can say about positive discriminant, that is, when D > 0:
If D is a perfect square, the quadratic equation will have two real, rational roots
If D is not a perfect square, the quadratic equation will have two real, irrational roots

And finally the formula for the roots of the quadratic equation is: \[\Large \frac{ -b \pm \sqrt{D} }{ 2a }\]