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

Question

Show the following quadratic equation by factorization method:
$\text{x}^2+\text{x}+\frac{1}{\sqrt{2}}=0$

✓

Answer

$\text{x}^2+\text{x}+\frac{1}{\sqrt{2}}=0$ We will apply discriminant rule,
$\text{x}=\frac{-\text{b}\pm\sqrt{\text{D}}}{2\text{a}}\ ...(\text{A})$
Where $D = b^2 - 4ac$
$=1^2-4.1.\frac{1}{\sqrt{2}}$$= 1 - 2\sqrt{2}$
From (A) $\text{x}=\frac{-1\pm\sqrt{-(2\sqrt{2}-1})}{2}$
$=\frac{-1\pm\sqrt{2\sqrt{2}-1\text{ i}}}{2}$ Thus,
$\therefore\text{x}=\frac{-1\pm\sqrt{2\sqrt{2}-1\text{ i}}}{2}$

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