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प्रश्न
\[4 x^2 + 1 = 0\]
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उत्तर
We have:
\[4 x^2 + 1 = 0\]
\[ \Rightarrow (2x )^2 - i^2 = 0\]
\[ \Rightarrow (2x )^2 - (i )^2 = 0\]
\[ \Rightarrow (2x + i) (2x - i) = 0\]
\[\Rightarrow (2x + i) = 0\] or \[(2x - i) = 0\]
\[\Rightarrow 2x = - i\] or \[2x = i\]
\[\Rightarrow\] \[x = - \frac{i}{2}\] or \[x = \frac{i}{2}\]
\[x = \frac{i}{2}\]
Hence, the roots of the equation are
\[\frac{1}{2}i \text { and } - \frac{1}{2}i\]
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