Question

\[4 x^2 + 1 = 0\]

Answer 1

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 

\[\frac{1}{2}i \text { and } - \frac{1}{2}i\]