This document explains the splitting the middle term method for solving quadratic equations by factorizing. It works through an example of solving the equation x^2 - 3x - 10 = 0. It shows that to use this method, you multiply the coefficient of x^2 (1) and the constant term (10) to get 10, then factorize 10 into 5 and 2 since you need to subtract. This allows writing the equation as (x - 5)(x + 2) = 0, revealing the solutions of x = 5 and x = -2.

1. SPLITTING THE
MIDDLE TERM
METHOD
WELCOME TO MATTER STUDY

2. FIND THE ROOTS OF THE QUADRATIC EQUATIONS
BY FACTORISATION:
(EX. 4.2 Q 1, CLASS 10TH NCERT)
 (i) 𝒙𝟐
−𝟑𝒙 − 𝟏𝟎 = 𝟎

3. NOW, WE TAKE THE FIRST PART
𝑥2 − 3𝑥 − 10 = 0
Rough Work / Think in Mind
As we know that, The general quadratic equation is
𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0
In Splitting the Middle Term Method,
Multiply a and c without considering sign
And make factors of multiplied result

4. Now Come to Our Example:
𝑥2 − 3𝑥 − 10 = 0
Step 1:
𝑥2
− 3𝑥 − 10 = 0
Multiply coefficient of 𝑿𝟐
(i.e. 1) and 10
1×10= 10
Now, we factorize this result
10 = 5,2
10 = 1,10
We consider 5 and 2, because we have to subtract

5. Step 2:
𝑥2 − 3𝑥 − 10 = 0
𝑥2 − 5 − 2 𝑥 − 10 = 0
𝑥2 − 5𝑥 + 2𝑥 − 10 = 0
NOW TAKING COMMON x AND 2
𝑥2 − 5𝑥 + 2𝑥 − 10 = 0
x(𝑥 − 5) + 2(𝑥 − 5) = 0
𝑥 − 5 𝑥 + 2 = 0
Our Roots Are:
X-5=0, x=5
X+2=0, x=-2

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