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Find the roots of the following quadratic equations by factorisation: (iv) 2x ^2 - x + 1 / 8

Q1.    Find the roots of the following quadratic equations by factorisation:

                (iv)    2x^2 -x + \frac{1}{8} = 0

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Given the quadratic equation: 2x^2 -x + \frac{1}{8} = 0

Solving the quadratic equations, we get

16x^2-8x+1 = 0

Factorisation gives, \Rightarrow 16x^2-4x-4x+1 = 0

\Rightarrow 4x(4x-1)-1(4x-1) = 0

\Rightarrow (4x-1)(4x-1) = 0

\Rightarrow x=\frac{1}{4}\ or\ \frac{1}{4}

Hence, the roots of the given quadratic equation are

 \frac{1}{4}\ and\ \frac{1}{4}.

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