Find the roots of the following quadratic equations by the factor… - Vidyadip

Question

Find the roots of the following quadratic equations by the factorisation method:
$21\text{x}^2-2\text{x}+\frac{1}{21}=0.$

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Answer

Given equation is $21\text{x}^2-2\text{x}+\frac{1}{21}=0$
On multiplying bt 21 on both sides, we get
$441x^2 - 42x + 1 = 0$
$441x^2 - (21x + 21x) + 1 = 0$ [by splitting the middle term]
$\Rightarrow 441x^2 - 21x - 21x + 1 = 0$
$\Rightarrow 21x(21x - 1) - 1(21x - 1) = 0$
$\Rightarrow (21x - 1)(21x - 1) = 0$
Now, $21\text{x}-1=0\Rightarrow\ \text{x}=\frac{1}{21}$ and $21\text{x}-1=0$
$\therefore\ \text{x}=\frac{1}{21}$
Hence, the roots of the equation $441x^2 - 42x + 1 = 0$ are $\frac{1}{21}$ and $\frac{1}{21}$.

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