Question 1(v)
Find the roots of the following quadratic equations by factorization:
$(v) 100 x^{2} - 20 x + 1 = 0$

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Solution

$(v) 100 x^{2} - 20 x + 1 = 100 x^{2} - 10 x - 10 x + 1$
(Splitting the middle term -20x as -10x-10x because $- 10 x \times - 10 x = 100 x^{2}$ )
$= 10 x (10 x - 1) - 1 (10 x - 1) = (10 x - 1)^{2}$
Roots of this equation are the values for which,
$(10 x - 1)^{2} = 0$
$∴ (10 x - 1) = 0 o r (10 x - 1) = 0$
$\Rightarrow x = \frac{1}{10} o r x = \frac{1}{10}$

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