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प्रश्न
9x2 + 4 = 0
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उत्तर
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
\[\frac{2i}{3} \text { and } - \frac{2i}{3} .\]
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