Question

Find the roots of the following
quadratic equation by factorisation
100x² - 20x+1=0​

Answer 1

100x² - 20 x + 1 = 0

Method 1 :

Splitting the middle term :

• Step 1 : We will multiply the coefficient of x² with constant term .
• Step 2 : Factorise the number obtained such that the sum of factor gives the second term .
• Step 3 : We can see if the factors need to be added or substracted to get the middle term by seeing the sign just before the constant term .

100 × 1 = 100 = 10 × 10 (10 + 10 = 20)

→ 100x² - (10 +10) x + 1 = 0

→ 100 x² - 10x -10x + 1 = 0

→ 10x (10x - 1) - 1 (10x - 1) = 0

→ (10x - 1)(10x - 1) = 0

10x - 1 = 0

10 x = 1

x = 1/10

Method 2 :

Using identity a² + b² - 2ab = (a - b)²

100x² - 20x +1 = 0

→ (10x)² - 2 × 10x × 1 + (1)² = 0

→ (10x -1)² = 0

10x -1 = 0

10 x = 1

x = 1/10

Answer 2

Solution:

100x2 - 20x + 1

= 100x2 - 10x - 10x + 1

= 10x ( 10x - 1 ) - 1 ( 10x - 1 )

= ( 10x - 1 ) ( 10x - 1 )

the roots of the equation are the values of x which ( 10x - 1 ) ( 10x - 1 ) = 0

therefore, 10x - 1 = 0

x = 1/10

so, the value of x is repeated twice

therefore ,the roots of 100x2 - 20x + 1 = 0 are

1/10 ,1/10