Question

find the roots of the quadratic equation 5 x square minus 2 root 10 x + 2 is equal to zero

Answer 1

Answer:

5 x^2 - 2 root 10 x + 2 = 0

x = - b + / - root b square - 4 ac / 2a ....

on solving this v get x = 2 by root 10....

Step-by-step explanation:

Answer 2

The roots are $\frac{\sqrt{2} }{\sqrt{5} }$  and $\frac{\sqrt{2} }{\sqrt{5} }$

Step-by-step explanation:

Given: The equation is $5x^{2} - 2\sqrt{10} x + 2 = 0$

To find: Roots of the equation

Solution:

$5x^{2} - 2\sqrt{10} x + 2 = 0$

$D = b^{2} - 4ac$

= $(-2\sqrt{10} )^{2} - 4 (5)(2)$

$= 40 - 40$

= 0

x = (-b ± D)/2a

= [(-2√10±√0]/ 10

= $\frac{2\sqrt{10} }{10}$

= $\frac{1\sqrt{10} }{5}$

=$\frac{\sqrt{10} \sqrt{5} }{5\sqrt{5} }$

= $\frac{\sqrt{50} }{5\sqrt{5} }$

= $\frac{\sqrt{25}\sqrt{2} }{5\sqrt{5} }$

= $\frac{5\sqrt{2} }{5\sqrt{5} }$

=$\frac{\sqrt{2} }{\sqrt{5} }$

Final answer:

Therefore the roots are $\frac{\sqrt{2} }{\sqrt{5} }$  and $\frac{\sqrt{2} }{\sqrt{5} }$

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