Solve Quadratic Equation by Factorisation, Formula and using Universal Calculator App

Download the Universal Calculator App for Android

Launch the App(mobile only) : Universal Calculator.

Solving a Quadratic equation

An equation of the format ax²+bx+c=0 where a != 0 is called quadratic equation.

1. Example: 3x²+5x+6 = 0
2. Example: x²+2=0
3. Example : 2x²+2x=4

Method 1: By factorization.

Here we factorize our equation so that it can be written in the format (x+a)(x+b)=0

We can then say that either

(x+a)=0 or (x+b)=0

Depending on which one we consider to be equal to zero, we would have two different values for x.

Let us try to understand this further by solving equation in example 3.

The given equation can be re-written in ax²+bx+c=0 format as shown below.

    =>2x²+2x-4=0

    =>a = 2, b = 2 & c = -4

Now to factorize this, we use grouping method.

In this method we split the co-efficient of x (b) such that their product is equal to the product of co-efficient of x² (a) and constant(c).

We have:

    =>co-efficient of x = 2,

    =>product of co-efficient of x² and Constant = 2*(-4) = -8.

Finding pairs of numbers whose product is -8 and eliminating the ones whose sum doesn’t equal to 2, we get

    4 * (-2) = -8.

    4 + (-2) = 2

We can now re-write our equation as:

    => 2x²+4x-2x-4=0

    => 2x(x+2)-2(x+2)=0

    => (x+2)(2x-2)=0

Therefore, the two roots are :

    1.  x+2=0

=> x=-2

    2. 2x-2 = 0

            =>2x=2

            =>x=1

Note: As all the numbers in the equation were divisible by 2, We could have also divided the equation by 2 before proceeding for factorization, however I didn't Since we wanted to cover example where co-efficient of x² is not equal to 1.
In real life scenarios, you should always try to get the smallest possible numbers for factorization by dividing the equation with appropriate number if it is possible to do so and then proceed with the steps explained above.

Method 2 : By using formula.

For any given Quadratic equation ax²+bx+c=0, the value of x can be found as 

x = 

=>our equation in example 3 can be re-written as 2x²+2x-4=0

=>a=2, b=2, c=-4

    =>x = 1, -2

 

Concept of Complex/imaginary root:

Let us understand this with an example: x²-2x=-26

Simplifying this equation to ax²+bx+c=0 format we get;

=> x²-2x+26=0

Substituting this in the formula we get;

As we cannot find the Square root of negative number, we can re-write the expressions as given below.

Since we don’t know the value of   √(-1)  The above roots are called imaginary roots.

They are represented in the below form, where a and b are real numbers and i=√(-1)  is an imaginary number.

x = a+bi , x = a-bi

also, a is called real part of the root and bi is called imaginary part of the root.

The numbers in the above format are also called as complex numbers.

=>x = 1+5i , x = 1-5i

 

Solving Quadratic equation by using Universal Calculator App:

Download the Universal Calculator App for Android & Launch the App(mobile only) : Universal Calculator.

1. Change the calculation mode to “Solve Quadratic Equation”.

2. Enter the equation as is and then click on Solve.

Refer to Screenshot below for further details.