The generic quadratic equation is y = a x2 + bx + c.
We know there are various methods to handle the quadratic equations.
- Completing the Square
- Quadratic Formula
Mastering all these techniques allow anyone studying maths to have the flexibility of choosing a better or suitable method that fits the nature of the question.
However, do note that if there is problem learning all these techniques at one go, click here to get some pointers.
What is the benefit?
Many maths questions are actually quadratic in expression. They may not appear so, but, on closer look, they are.
- 3 cos2 A + 2cosA + 4 = 0
- 2 (log Y)2 + 2(logY) + 3 = 0
- 4x + 3(2x) - 5 = 0
- 5x-2 - 7x-1 - 6 = 0
Being able to handle the generic quadratic equation solving means having the potential to solve numerous other types of quadratic equations as listed above.
What is the obstacle if you still cannot map the quadratic solving method to the other types of expressions?
- Stare at the given expression
- Identify the terms that matches the x2 format.
- Identify the other two terms through the "x" format and pure number format.
- After re-writing the questions in the generic quadratic form, apply any of the method to solve this quadratic equation.
And that's all.
Simple isn't it?
Thus, mastering any one method of handling quadratic equation allows anyone to solve many other types of quadratic equations. Therefore, it is worth the time and effort to know solving these type of mathematical expression.
Let's look into this example
The first term can be modified to 5(x-1)2.
The second term can be modified to 3(x-1).
The last term will be obviously the pure number "2".
Selecting the use of quadratic formula, we can say that a = 5, b= -3 and c = -2.
Next, just apply the quadratic formula and you are close to the two answers (roots) of the equation,
x-1 = -4/10 or 1. Clear?
If not, read again... Our brain needs some mental exercise at times.