Finding roots of quadratic equation using the quadratic formula
In the year 10 program, we learnt how to find the discriminant and how to find the roots using it. Now, we will at how we can find the roots using the quadratic formula as well as learning to prove it by completing the square.
Quadratic Equation proof
We will now prove the quadratic equation by completing the square. We have a general equation on the left where a, b and c are coefficients. By completing the square, we add and subtract b^2/4a to get:
As we learnt in the year 10 program, if the discriminant > 0
A positive discriminant would have 2 real roots. An example of a graph of a quadratic equation with a positive discriminant is shown on the left.
if the discriminant = 0
If the discriminant is equal to 0, then there is only one real solution. An example of a graph of a quadratic equation with a discriminant = 0 is shown on the left.
if the discriminant < 0
A negative discriminant would have no real roots. An example of a graph of a quadratic equation with a negative discriminant is shown on the left.