This week in math 11, we learned about the role of the discriminant in quadratic equations.

The discriminant is the radicand in the quadratic formula:

The discriminant tells us the nature of the roots of the quadratic equation, which basically means it tells us how many roots there are, if they are rational or not, and if they are real or not.

– there will be 2 distinct roots

– there are no real roots/unreal roots

– there is 2 equal roots/one number

= perfect square- it is rational

= non-perfect square- it is irrational

For an example we are going to use a basic quadratic trinomial and find it’s nature of roots

Now we find the discriminant with the formula 

(a=1, b=-4, c=5)

 

 

So we know that since the discriminant is less than 0, there are no real roots and that the root is unreal.