As we have talked about earlier, alpha = A – B and
beta = A + B where A and B are as shown, A=-b/2a & B=sq rt D/2a. Thus, when we add,
alpha + beta = 2A = – b/a and
alpha x beta = A^2 – B^2 = c/a
We have shown a few solved examples and there a few practice exercise for you to attempt.
Make a practice of finding the Sum & Product of the roots and also the Discriminant.
In mathematics we look at an entity (an expression) every which way, especially we look at the obverse side e.g. if it is a right angled triangle, the length of the three sides will abide by Pythagoras’ Theorem. To state the same thing obversely, we can state that if the three sides of any triangle follow the Pythagoras’ Theorem, the triangle is a right angled triangle.
Similarly here, if we are given a quadratic equation, we can find the sum & product of the two roots.
Here we show its obverse theorem i.e. if we are given the sum and product of the two roots of a quadratic, we can write down the quadratic equation like this:
Thus knowing this, we can solve the problem shown in the diagram.