Question

Find the root of the following quadratic equations by the factorisation method:

`21x^2 - 2x + 1/21` = 0

Answer 1

Given equation is `21x^2 - 2x + 1/21` = 0

On multiplying by 21 on both sides, we get

`441x^2 - 42x + 1` = 0

`441x^2 - (21x + 21x) + 1` = 0   ....[By splitting the middle term]

⇒ `44x^2 - 21x - 21x + 1` = 0

⇒ `21x(21x - 1) - 1(21x - 1)` = 0

⇒ `(21x - 1)(21x - 1)` = 0

Now `21x - 1` = 0

⇒ `x = 1/21` and `21x - 1` = 0

∴ `x = 1/21`

Hence the roots of the equation `441x^2 - 42x + 1` = 0 are `1/21` and `1/21`.