Given a quadratic equation with roots and , we have:
How do we prove this? It is actually due to the quadratic formula!
Recall that the quadratic formula gives the roots of the quadratic equation as:
Now, we can let
In the above proof, we made use of the identity
The above formulas are also known as Vieta’s formulas (for quadratic). There we have it, this is how we prove the formula for the sum and product of roots!