Question

\[x^2 - 2x + \frac{3}{2} = 0\]

Answer 1

\[x^2 - 2x + \frac{3}{2} = 0\]

\[ \Rightarrow x^2 - 2x + 1 + \frac{1}{2} = 0\]

\[ \Rightarrow \left( x - 1 \right)^2 - \left( \frac{1}{\sqrt{2}}i \right)^2 = 0\]

\[ \Rightarrow \left( x - 1 + \frac{1}{\sqrt{2}}i \right) \left( x - 1 - \frac{1}{\sqrt{2}}i \right) = 0\]

\[\Rightarrow \left( x - 1 - \frac{1}{\sqrt{2}}i \right) = 0\]  or,\[\left( x - 1 + \frac{1}{\sqrt{2}}i \right) = 0\]

\[\Rightarrow x = 1 + \frac{1}{\sqrt{2}}i\] or, \[x = 1 - \frac{1}{\sqrt{2}}i\]

Hence, the roots of the equation are  \[1 \pm \frac{1}{\sqrt{2}}i\] .