Quadratic formula: Video Tutorial

In this tutorial I'm sharing two videos which is emphasizing quadratic formula, To save time Check out following videos​ for better understanding of the topic Quadratic formula, 

Quadratic formula: Video Tutorial

                                          

and

If you want me to share some more do let me know via comment, I would like to hear from you.

Quadratic Formula

Quadratic Formula 

Quadratic Formula is also known as "Shreedhracharya veedhi".

 • What is Quadratic Formula ?

Quadratic Formula is a tool to find roots of any Quadratic equation instead of Middle term splitting method, Quadratic Formula can also be used to evaluate roots.

 •  Standard form of Quadratic equation is : 

     ax² + bx + c  

hence Quadratic Formula states as -
 

•    x = [ -b ± √(b² - 4ac)]  / 2a

 • Discriminant:

Numerator part of this formula ( except "-b" ) known as discriminant, and gives a very useful information about nature of roots and denoted by "D" :

D = (b² - 4ac)

• following three conditions​ can be expected from Solution of D i.e.

• if,  D > 0 then :  existed roots are real but                                    distinct
• if,  D = 0 then :  existed roots are real and                                     equal
• if,  D < 0 then :  roots doesn't exist or                                           imaginary

 • From this test we can guess out what kind of roots any given Quadratic equation posses without evaluating.

 • Example :

Q. 2x² + 3x - 5

sol. by comparing from standard form of equation we have 

        a= 2 ; b= 3 ; c = -5

Test : with Discriminant 

            D = b² - 4ac

             = 3² - 4× 2×(-5)

             = 9  - (-40)

             = 9 +40  = 49 >0

means equation has real and distinct roots.

now by applying Quadratic Formula:

x = [ -3 ± (49)] / 2× 2

   = [ -3 ± 49 ] /4

by +value :

x = [-3 + 49] /4

   = 46/4  

by - value :

x = [ -3 - 49]/ 4

   = -52/4.

Hope this post has proven very useful for you, Do let me inform with comments, Feel free to share.

and also

Check out our other related posts :

• Middle term splitting method: video tutorial

• Quadratic equations: by Mr. Sumit Verma

• 3 Easy steps to solve Long Division

How to solve Quadratic equations By MTS

when anybody tend to solve any Quadratic equation, the first method which comes in his or her mind is solving that equation by MTS method.

Middle term Splitting Method

MTS means Middle term splitting.

standard form of Quadratic equation is 

ax² + bx + c 

i.e. first term or the highest degree of equation must be 2, then a linear term and then constant term should be arranged.

here Middle term is bx, this should be splitted.

• How To Apply MTS -

MTS means middle term should be splitted,

But the question us HOW???

Here is the answer cum method step by step -

• Multiply 1st and the last numbers, put this aside.
• Now pick the middle term and try to split this into two parts such that when those terms added/subtracted the resultant should be the, same middle term and when those terms are multiplied the resultant should be equal to the resultant which occurred​ in first step.
• That's why this method is known as MTS.
• Now we'll have four terms, among those four terms make the group of first two and last two.
• Take the common out from those groups.
• Do remember..!!
• After taking common out the values in the Brackets should be equal otherwise this may become sign of wrong solution.
• Now we'll have two brackets take one and form an another bracket using values which were lying outside the Brackets.
• Finally we'll have two Brackets which are the​ required factorisation of given equation.

Check this image based solutions

For an example :-

x² + 5x + 6

multiplying 1st and last term  x² × 6 = 6x²

Splitting  5x

                   2x and 3x can be splitting terms

                   as    2x + 3x  =  5x

                   and  2x × 3x = 6x²

hence 

x² + 5x + 6

x² + 2x + 3x + 6

by grouping 

(x² + 2x ) + ( 3x + 6)

taking common out

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

do remember brackets are similar hence we are proceeding correctly

final step 

( x+ 2) ( x+ 3)

ans.

• Further more if we are to ask to find the factors of the equation also.

Then We have to apply MTS first and have to find brackets as well then these brackets individually give factors respectively for this purpose see below -

now 

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

either  ( x+ 2) = 0  ; x = -2

or         ( x + 3) = 0 ; x = -3

• See video for better understanding.
• Try another method
• Try Completing the square method to solve quadratic equations

Check and try to solve at your own examples given below -

Yes..!! for convenience to you answers are written against the equations.

Still if you are finding difficulties, I'll be pleased to hear from you.

Feel free to share this post.

How to solve Quadratic Equation (video)?

MIDDLE TERM SPLITTING METHOD

this is one of the most effective way to solute quadratic equations.

But on other aspect for those equations which are found to be difficult to solve, we have to look onto another methods which includes 

• Completing the square method 
• Quadratic Formula 

I'll take these one by one in upcoming posts but for today in this post check out the following video ( Found shareable) which Emphasising QUADRATIC EQUATIONS and their basics

explained by Mr.Sumit Verma

Check out our other popular posts

• Top 8 helpful Math Topic

• Divisibility Rules

And also let me know how you have found above video to explain middle term splitting methodby comments.