Factorization Method Class 10th

Introduction

In the Factorization Method, we factorize the quadratic equation and put each factor equal to zero and then find the values of x. These values of x are the solution of the quadratic equation and are called the roots of the quadratic equation.

FACTORIZATION METHOD

This can be understood by the following examples.

Examples

Example – 1) Find the roots of the quadratic equation x2 + 5x + 6 = 0 by factorization method.

Solution – given equation   x2 + 5x + 6 = 0

Step (1) Comparing the equation with the standard form ax2 + bx + c = 0

a = 1, b = 5, c = 6

We take      a⨯c = 1⨯6 = 6    and      b = 5

Step (2) Now we have to take two numeric values so that their sum should be equal to b i.e., 5 and their multiplication should be equal to a⨯c i.e., 6. So, we take the numbers 2 and 3.

Note – if it is difficult to find the two numeric values, we can factorize the term a⨯c and make pair to get it easily. 

Step (3) Now check

2+3 = 5 and 2⨯3 = 6 (these values satisfy)

Step (4) Now, break the middle term of the equation x2 + 5x + 6 with the help of the above sum 2+3 = 5

x2 + (2+3)x + 6 = 0

x2 + 2x + 3x + 6 = 0

Step (5) Now take common terms out from the first two terms and last two terms.

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

(x+2) is again a common term so,

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

Step (6) Now putting each factor equals to zero.

(x+2) = 0   and    (x+3) = 0

x = -2    and         x = -3 Ans.

Both the values of x are the solution of the given quadratic equation and are called the roots of this equation.

We can check our answer by putting the values of x in the given quadratic equation.

x2 + 5x + 6 = 0

at x = -2,                                                          

(-2)2 + 5(-2) + 6 = 0                                         

4 – 10 + 6 = 0                                                  

– 6 + 6 = 0                                                         

0 = 0                                                                 

LHS = RHS                                                    

at x = -3,

(-3)2 + 5(-3) + 6 = 0

9 – 15 + 6 = 0

– 6 + 6 = 0

0 = 0

LHS = RHS

At both the values, LHS = RHS it means our answer is correct.

Example – 2) Find the roots of the quadratic equation 2x2 – 5x + 3 = 0 by factorization method.

Solution – 2x2 – 5x + 3 = 0             Here, a⨯c = 2⨯3 = 6 and b = -5

2x2 – (2+3)x + 3 = 0                        two numeric values -2 and -3

2x2 – 2x – 3x + 3 = 0                       -2⨯(-3) = 6 and -2 + (-3) = -2 – 3 = -5 

2x(x-1) -3(x-1) = 0

(x-1) (2x-3) = 0

(x-1) = 0   and   (2x-3) = 0

x = 1    and       x = 3/2     

Thus, the roots of the quadratic equation 2x2 – 5x + 3 = 0 are x = 1 and x = 3/2.    Ans.

Factorization Method Class 10th in Hindi

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