# SOLVING QUADRATIC EQUATIONS BY FACTORING METHOD

Solving Quadratic Equations by Factoring Method :

Here we are going to see how to solve quadratic equations by factoring method.

We follow the steps provided below to solve a quadratic equation through factorization method.

Step 1 :

Write the equation in general form ax2 +bx +c = 0

Step 2 :

By splitting the middle term, factorize the given equation.

Step 3 :

After factorizing, the given quadratic equation can be written as product of two linear factors.

Step 4 :

Equate each linear factor to zero and solve for x. These values of x gives the roots of the equation. ## Solving Quadratic Equations by Factoring Method - Questions

Question 1 :

Solve the following quadratic equations by factorization method

(i) 4x2 − 7x − 2 = 0

Solution :

Product of coefficient of x and constant is -8

Now, we have to decompose -8 as product of two term, such that the product of those numbers must be -8 and simplified value must be equal to -7.

Since the middle and last terms are negative, we have to put negative sign for large factor. (4x + 1) (x - 2)  =  0

4x + 1  =  0   (or)   x - 2  =  0

4x  =  -1   (or)    x = 2

x  =  -1/4   (or)  x = 2

Hence the solutions are -1/4 and 2.

(ii) 3(p2 −6) = p(p + 5)

Solution :

3p2 −18 = p2 + 5p

3p2 - p2 - 5p - 18  =  0

2p2 - 5p - 18  =  0

Since the middle and last terms are negative, we have to put negative sign for large factor. (2x + 9) (x - 2)  =  0

2x + 9  =  0    (or)  x - 2  =  0

2x  = -9    (or)  x = 2

x  =  -9/2

Hence the solutions are -9/2 and 2.

(iii)  √(a(a −7)) = 3 2

Solution :

√(a(a −7)) = 3 2

Taking squares on both sides,

[√(a(a −7))]2  =  (32)2

a (a - 7)  =  9(2)

a2 - 7a  =  18

a2 - 7a  - 18  =  0

Since the middle and last terms are negative, we have to put negative sign for large factor. (x + 1) (2x - 9)  =  0

x + 1  =  0     (or)   2x - 9  =  0

x  =  -1    (or)  2x  =  9

x  =  9/2

Hence the solutions are -1 and 9/2. After having gone through the stuff given above, we hope that the students would have understood, "Solving Quadratic Equations by Factoring Method".

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