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
Quadratic equation

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

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

Factoring expression
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.

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