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

Given:

Given quadratic equation is \( 21 x^{2}-2 x+\frac{1}{21}=0 \).

To do:

We have to find the roots of the given quadratic equation.

Solution:

\( 21 x^{2}-2 x+\frac{1}{21}=0 \)

Multiplying by 21 on both sides, we get,

$441 x^{2}-42 x+1=0$

$441 x^{2}-(21 x+21 x)+1=0$

$441 x^{2}-21 x-21 x+1=0$

$21 x(21 x-1)-1(21 x-1)=0$

$(21 x-1)(21 x-1)=0$

$21 x-1=0$ or $21 x-1=0$

$x=\frac{1}{21}$ or $x=\frac{1}{21}$

Hence, the roots of the given quadratic equation are $\frac{1}{21}, \frac{1}{21}$.   

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Updated on: 10-Oct-2022

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