FACTORING METHOD SOLVING QUADRATIC EQUATIONS

Factoring Method Solving Quadratic Equations :

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.  

Factoring Method Solving Quadratic Equations - Questions

Question 1 :

Solve the following quadratic equations by factorization method

2x2 + 7x + 52 = 0

Solution :

Product of coefficient of x and constant is 10.

2x2 + 2x + 5x + 52 = 0

2  =  2

2x(x + 2) + 5(x + 2)  =  0

(√2x + 5) (x + 2)  =  0

2x + 5  =  0     (or)   x + 2  =  0

 2x  =  -5   (or)  x  =  -2

  x  =  -5/2    

(v)  2x2 − x + (1/5)  =  0

Solution :

(10x2 − 5x + 1)/5  =  0

10x2 − 5x + 1  =  0

10x2 − 10x  + 5x + 1  =  0

10x (x + 1) + 1(5x + 1)  =  0

(10x + 1)   (5x + 1)  =  0

10x + 1  =  0     (or)  5x + 1  =  0

10x  =  -1    (or)  5x  =  -1

x  =  -1/10   (or)  x  =  -1/5

Hence the solutions are -1/10 and -1/5.

Question 2 :

The number of volleyball games that must be scheduled in a league with n teams is given by G (n) = (n2 - n)/2 where each team plays with every other team exactly once. A league schedules 15 games. How many teams are in the league?

Solution :

Number of games scheduled  =  15

(n2 - n)/2   =  15

n2 - n   =  30

n2 - n - 30  = 0

n2 - 6n + 5n - 30  = 0

n(n -6) + 5(n - 6)  =  0

(n - 6)(n + 5)  =  0

n - 6  =  0  and  n + 5  =  0

 n  =  6    and  n = -5

Hence 6 teams are in the league.

After having gone through the stuff given above, we hope that the students would have understood, "Factoring Method Solving Quadratic Equations". 

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