Solve: x^2 - 2x + 3 2 = 0 - Vidyadip

Question

Solve: ${x^2} - 2x + \frac{3}{2} = 0$

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Answer

Here ${x^2} - 2x + \frac{3}{2} = 0$
Comparing the given quadratic equation with $ax^2 + bx + c = 0$ we have,
a=1,b=-2, $c = \frac{3}{2}$
$\therefore x = \frac{{ - ( - 2) \pm \sqrt {{{( - 2)}^2} - 4 \times 1 \times \frac{3}{2}} }}{{2 \times 1}}$$ = \frac{{2 \pm \sqrt {4 - 6} }}{2} = \frac{{2 \pm \sqrt 2 }}{2}$
$ = \frac{{2 \pm \sqrt 2 i}}{2} = 1 \pm \frac{{\sqrt 2 }}{2}i$
Thus $x = 1 + \frac{{\sqrt 2 }}{2}i$ and $x = 1 - \frac{{\sqrt 2 }}{2}i$

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