Show the following quadratic equation by factorization method: 5x… - Vidyadip

Question

Show the following quadratic equation by factorization method: $\sqrt{5}\text{x}^2+\text{x}+\sqrt{5}=0$

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Answer

$\sqrt{5}\text{x}^2+\text{x}+\sqrt{5}=0$ We will apply discriminant rule, $\text{x}=\frac{-\text{b}\pm\sqrt{\text{D}}}{2\text{a}}\ ...(\text{A})$
$D = b^2 - 4ac =1^2-4.\sqrt{5}.\sqrt{5}$ = 1 - 20 = -19 From (A) $\text{x}=\frac{-1\pm\sqrt{-19}}{2.\sqrt{5}}$ $=\frac{-1\pm\sqrt{-19}\text{ i}}{2\sqrt{5}}$
Thus, $\therefore\text{x}=\frac{-1\pm\sqrt{19}\text{ i}}{2\sqrt{5}}$

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