Obtain the roots of the following equation us | vedclass

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Question

(A) Given equation: $5x^{2} - 4x - 10 = 0$.Divide the entire equation by $5$ to make the coefficient of $x^{2}$ equal to $1$:$x^{2} - \frac{4}{5}x - 2

Vedclass · Accepted Answer

$\frac{2 - 3\sqrt{6}}{5}, \frac{2 + 3\sqrt{6}}{5}$

Vedclass · Answer

(A) Given equation: $5x^{2} - 4x - 10 = 0$.Divide the entire equation by $5$ to make the coefficient of $x^{2}$ equal to $1$:$x^{2} - \frac{4}{5}x - 2 = 0$.Shift the constant term to the right side:$x^{2} - \frac{4}{5}x = 2$.Add the square of half the coefficient of $x$ (which is $(\frac{1}{2} 	imes \frac{4}{5})^{2} = (\frac{2}{5})^{2} = \frac{4}{25}$) to both sides:$x^{2} - \frac{4}{5}x + \frac{4}{25} = 2 + \frac{4}{25}$.Rewrite the left side as a perfect square:$(x - \frac{2}{5})^{2} = \frac{50 + 4}{25} = \frac{54}{25}$.Take the square root of both sides:$x - \frac{2}{5} = \pm \sqrt{\frac{54}{25}} = \pm \frac{3\sqrt{6}}{5}$.Solve for $x$:$x = \frac{2}{5} \pm \frac{3\sqrt{6}}{5} = \frac{2 \pm 3\sqrt{6}}{5}$.Thus,the roots are $\frac{2 - 3\sqrt{6}}{5}$ and $\frac{2 + 3\sqrt{6}}{5}$.

Obtain the roots of the following equation using the method of 'completing the square': $5x^{2} - 4x - 10 = 0$.

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