The term ALTERNATIVE simply means another option. Unlike the formula method and completing the square method, alternative method of solving quadratic equation requires no formula. Quadratic equation is a very common question examiners test candidates or students in any examination most especially WAEC, NECO and JAMB. This is a compulsory question that students or candidates come across every academic session in WAEC or NECO Senior Secondary Certificate Examination (SSCE). In one of our posts, we broke down the steps and cited with examples on how to solve quadratic equation using completing the square method. In this post, we will go further on how to solve quadratic equation using alternative method.

Students upon selecting their career line opt for courses that do not require mathematics as a means of admission into tertiary institutions simply because they are scared of mathematics, this is a wrong mentality as it could deter them from studying the right courses. Mathematics is simple, In fact it is one of the easiest subjects offered in junior and secondary schools only if you are willing to learn and concentrate. All that is required is the application of your common sense, reasoning ability and focus.

The West African Examination Council (WAEC) as well as the National Examination Council (NECO) test senior students every academic session on quadratic equations and specifically make it mandatory for students to solve quadratic equations using either completing the square method, alternative method or graphical method because students intentional shy away from using any of the above methods of solving quadratic equation due to it many steps, rather, they prefer using the *Formula method*. The positives from knowing that a particular question must come out in an examination should give you the extra boost and preparedness hence higher score.

*For those who do now know how to use the alternative method of solving quadratic equation can learn the step by step breakdown below:*

Basically, there are the 4 methods of solving quadratic equations, namely:

- Alternative method
- Formula method (Almighty Formula)
- Graphical method
- Completing the square method.

**Best Form of Solving Quadratic Equations Using Alternative Method**

For the sake of this post, we are going to teach you the simplest method on how you can solve any quadratic equations using alternative method amongst the other methods listed above.

Solving a Quadratic equation using alternative method do not require any formula.

**NOTE:** If you have not been directed by your examiner on the exact method to be adopted in solving quadratic equation, the* alternative method* or *formula method* are the simplest means of solving quadratic equation, so i will advice you adopt any of them since it saves time and guarantee full marks apportioned to the question.

With the steps I shall be putting you through below, you should apply it in solving any quadratic equation in WAEC, NECO or any examination you are tested on.

**EXAMPLE 1:** Solve this quadratic equation using Alternative method: *3x² + 14x + 8= 0*

Firstly we find the product of the first and the last term of the equation.

:. 3x² × 8 = 24x²

We look for numbers to multiply to give 24x² and at the same time add or subtract to give 14x as the case present itself.

That number is 12x & 2x

:. (12x) × (2x) = 24x²

:. 12x + 2x = 14x

:. 3x² + 14x + 8 = 0

Also the same as;

:. 3x² + 12x + 2x + 8

Our next step is to group by taking brackets..

(3x² +12x) +(2x + 8)

We now factorize to enable us eliminate a factor from 2 common factors.

3x(x+4) + 2(x+4)

Note (x+4) is common to both LHS and RHS

:. Only one factor is required, which now results in;

(3x + 2)(x+ 4)= 0

:. (3x+2)=0, :. x = -⅔

:. (x + 4)=0, :. x = -4.

Now we can say that the values of x are -⅔ or -4

I believe the above example is well explained. You could be faced with this type of alternative equation question anywhere and making use of the above steps can guarantee you full marks on any quadratic equation question that mandates you solve it using alternative method.

Hope the above is well understood? If you still have any questions as regards how to solve quadratic equations using alternative method in WAEC, NECO, JAMB or any test, please feel free to reach through to us via the comment section below and we shall respond to all questions accordingly.