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 = b² - 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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