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Question
4x2 − 12x + 25 = 0
Solution
We have:
\[4 x^2 - 12x + 25 = 0\]
\[ \Rightarrow 4 x^2 - 12 x + 9 + 16 = 0\]
\[ \Rightarrow (2x )^2 + 3^2 - 2 \times 2x \times 3 - (4i )^2 = 0\]
\[ \Rightarrow (2x - 3 )^2 - (4i )^2 = 0\]
\[ \Rightarrow (2x - 3 + 4i) (2x - 3 - 4i) = 0 [ a^2 - b^2 = (a + b) (a - b)]\]
\[\Rightarrow (2x - 3 + 4i) = 0\] or, \[(2x - 3 - 4i) = 0\]
\[\Rightarrow 2x = 3 - 4i\] or, \[2x = 3 + 4i\]
\[\Rightarrow x = \frac{3}{2} - 2i\] or, \[x = \frac{3}{2} + 2i\]
Hence, the roots of the equation are \[\frac{3}{2} - 2i \text { and } \frac{3}{2} + 2i\] .
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