|
|
Today I am going to show you a cool trick how to check to make sure your answers for the solution of a quadratic equation is correct without plugging the values back into the equation. Have you ever heard the term “Sum of the Roots and the Product of the Roots”? Well if you have not, today I am going to teach you it. The symbol I will use for alpha is (K*) and for beta is (V*). Where (K*) is one solution and (V*) is the other solution.
The sum of the roots is alpha plus beta (K* +V*) and the product of the roots is (K* x V*). This method works like this, (K* + V*) must be equal to (–b/a) and (K* x V*) must be equal to (c/a). Are you still confused? Okay, let’s look a question I had previously done.
14x^2 – 13x – 27 = 0
In this case a = 14, b = - 13 and c = -27
We have already solved the equation to produce solutions of x = 27/14 and x = - 1
The Visual method showed you how to solved it, but what if you forgot the visual method? (The conditions are in red above)
Let’s apply the sum of the roots! In the equation (- b/a) equals to (- (-13/14)) which is equal to (13/14).
The sum of the roots (K* + V*) equals to ( 27/14 + (-1)) = ( 13/14)
Therefore the first condition is satisfied!
Let’s apply the product of the roots! In the equation (c/a)=(-27/14).
The product of the roots (K* x V*) = ( (27/14) x (-1)) = (-27/14)
Therefore the second condition is satisfied!
If these two conditions are satisfied, then your solutions are correct and there will be no need to plug in your values to double check you answer. This method applies for all quadratic equations.
|
No responses found. Be the first to respond and make money from revenue sharing program.
|