Question

4x² − 12x + 25 = 0

Answer 1

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