Question

Find the roots of this quadratic equation
${5x}^{2} - 6x - 2 = 0$
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Answer 1

Given equation :  

⇒ 5x2 - 6x  = 2

Dividing above equation by 5

 $\sf\small \\ \Rightarrow x^2-\dfrac{6x}{5}=\dfrac25$

On adding (⅗)^2 both sides :

$\sf\small \\ \Rightarrow x^2-2\times\dfrac{3x}{5} +\left (\dfrac35 \right )^2=\dfrac25$

Above equation is of the form ( a2- 2ab + b2)   = (a + b)2

$\sf\small \\\Rightarrow \left (x-\dfrac35 \right )^2=\dfrac{2}{5}+\dfrac{9}{25}=\dfrac{19}{25}$

$\sf\Rightarrow \left (x-\dfrac35 \right )=\sqrt{\dfrac{19}{25}}\\\\\\\\\sf\Rightarrow \left (x-\dfrac35 \right )=\pm \dfrac{\sqrt{19}}{5}$

$\sf\Rightarrow x=\dfrac{\sqrt{19}}{5}+\dfrac35 \quad or \quad x=\dfrac{-\sqrt{19}}{5}+\dfrac35$

$\sf x=\dfrac{\sqrt{19}+3}{5} \quad or \quad \sf x=\dfrac{-\sqrt{19}+3}{5}$

Hence, your answer is verified.

Answer 2

Answer:

There are many ways to find the roots of quadratic equation but I have choosen it. I hope you will understand.