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Question
Find the roots of the following quadratic equation by the factorisation method:
`21x^2 - 2x + 1/21 = 0`
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Solution
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`.
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