Show the following quadratic equation by factorization method: x^… - Vidyadip

Question

Show the following quadratic equation by factorization method:
$\text{x}^2 +2\text{ x} +\frac{3}{2}=0$

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Answer

$\text{x}^2 +2\text{ x} +\frac{3}{2}=0$
We will apply discriminant rule, $\text{x}=\frac{-\text{b}\pm\sqrt{\text{D}}}{2\text{a}}\ ...(\text{A})$
Where $D = b^2 - 4ac$ $=(-2)^2-4(1)\Big(\frac{3}{2}\Big)$ $= 4 - 6 = -2$
From (A) $\text{x}=\frac{-(-2)\pm\sqrt{-2}}{2(1)}$ $=\frac{2\pm\text{i}\sqrt{2}}{2}$
$=1\pm\frac{\text{i}}{\sqrt{2}}$
Thus, $\therefore\text{x}=1\pm\frac{\text{i}}{\sqrt{2}}$

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