FACTORING METHOD SOLVING QUADRATIC EQUATIONS

The following steps will be useful to solve a quadratic equation by factoring.

Step 1 :

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

Step 2 :

If the coefficient of x² is 1, we have to take the constant term and split it into two factors such that the product of those factors must be equal to the constant term and simplified value must be equal to the middle term.

If the coefficient of x² is not 1, we have to multiply the constant term along with the coefficient of x².Split the product into two factors.

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.  

How to assign signs for the two factors ?

Solved Questions

Question 1 :

Solve the following quadratic equations by factorization method :

√2x² + 7x + 5√2 = 0

Solution :

Product of coefficient of x²  and constant is 10.

√2x² + 2x + 5x + 5√2 = 0

2  =  √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    

Question 2 :

Solve the following quadratic equations by factorization method :

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 3 :

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.

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