Question

9x² + 4 = 0

Answer 1

Given: 

\[9 x^2 + 4 = 0\]

\[9 x^2 + 4 = 0\]

\[ \Rightarrow (3x )^2 + 2^2 = 0\]

\[ \Rightarrow (3x )^2 - (2i )^2 = 0\]

\[ \Rightarrow (3x + 2i) (3x - 2i) = 0 [( a^2 - b^2 ) = (a + b) (a - b)]\]

\[\Rightarrow (3x + 2i) = 0\] or,\[(3x - 2i) = 0\]

\[\Rightarrow 3x = - 2i\] or \[3x = 2i\]

\[\Rightarrow x = - \frac{2i}{3}\] or  \[x = \frac{2i}{3}\]

Hence, the roots of the equation are 

\[\frac{2i}{3} \text { and } - \frac{2i}{3} .\]