Show the following quadratic equation by factorization method: 2x… - Vidyadip

Question

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

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Answer

$\sqrt{2}\text{x}^2+\text{x}+\sqrt{2}=0$ We will apply discriminant rule, $\text{x}=\frac{-\text{b}\pm\sqrt{\text{D}}}{2\text{a}}\ ...(\text{A})$
Where $D = b^2 - 4ac =1^2-4.\sqrt{2}.\sqrt{2}$ = 1 - 8 = -7 From (A) $\text{x}=\frac{-1\pm\sqrt{-7}}{2.\sqrt{2}}$ $=\frac{{-1}\pm\sqrt{7}\text{ i}}{2\sqrt{2}}$
$\therefore\text{x}=\frac{-{1}\pm\sqrt{7}\text{ i}}{2\sqrt{2}}$

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