Question

Find the roots of the following quadratic equation 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

441x² – 42x + 1 = 0

⇒ 441x² – (21x + 21x) + 1 = 0   ....[By splitting the middle term]

⇒ 44x² – 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 441x² – 42x + 1 = 0 are `1/21` and `1/21`.