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

Question

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

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Answer

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

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