## SOLVE A QUADRATIC EQUATION BY FACTORING

Solve a quadratic equation by factoring :

Usually we have three methods to solve a quadratic equations.

(1)  Factoring

(3)  Completing the square method

Here we are going to see how to solve a quadratic equation by using the method factoring.

To factor a quadratic equation which is in the form ax² + bx + c = 0, we have to follow the steps given below.

## Solving quadratic equations in which the value of a is 1

• If it is 1, then we have to take the constant term and split it into two factors.
• In which the product of two factors must be equal to the constant term and the simplified value of those factors equal to the middle term, that is coefficient of x.
• Write each factors in the form (x + a) (x + b) according to the sign.
• Set each factors equal to zero to get the value of x.

## Solving quadratic equations in which the value of a is not 1

• Multiply the coefficient of x² and constant term.
• Split this product into two factors such that their sum is equal to the coefficient of x .
• Divide each factors by the coefficient of x².
• If it is possible we may simplify, otherwise we have to write the denominator along with x.
• write each factors in the form (x + a) (x + b).
• Set each factors equal to zero to get the value of x.

## Solve a quadratic equation by factoring - Examples

Example 1 :

Solve x² + 9 x + 14  =  0

Solution :

Since the coefficient of x² is 1, split the constant term that into two parts.

14  =  ⋅ 7, 2 + 7  =  9

x² + 9 x + 14  =  0

(x + 2) (x + 7)  =  0

x - 2  =  0     x + 7  =  0

x  =  2, x  =  -7

Hence the solution is {2, -7}

Example 2 :

Solve x² - 9 x + 14  =  0

Solution :

Since the coefficient of x² is 1, split the constant term that into two parts.

14  =  -2 ⋅ (-7) , -2 - 7  =  -9

x² - 9 x + 14  =  (x - 2) (x - 7)

(x - 2) (x - 7)  =  0

x - 2  =  0     x - 7  =  0

x  =  2, x  =  7

Hence the solution is {2, 7}

Example 3 :

Solve x² + 2 x - 15  =  0

Solution :

Since the coefficient of x² is 1, split the constant term that into two parts.

-15  =  -3 ⋅ 5 , -3 + 5  =  2

x² + 2 x - 15  =  (x - 3) (x + 5)

(x - 3) (x + 5)  =  0

x - 3  =  0     x + 5  =  0

x  =  3, x  =  -5

Hence the solution is {3, -5}

Example 4 :

Solve x² - 2 x - 15  =  0

Solution :

Since the coefficient of x² is 1, split the constant term that into two parts.

-15  =  -5 ⋅ 3 , -5 + 3  =  -2

x² - 2 x - 15  =  (x - 5) (x + 3)

(x - 5) (x + 3)  =  0

x - 5  =  0     x + 3  =  0

x  =  5, x  =  -3

Hence the solution is {-3, 5}

After having gone through the stuff given above, we hope that the students would have understood "Solve a quadratic equation by factoring"

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