Question

the sum of roots of
$\sqrt{3} x + 6 \sqrt{3x + 9 = 0}$
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Answer 1

Question :-

Find the sum of roots of ,

$\sqrt{3} x + 6 \sqrt{3x + 9 = 0}$

Answer :-

$\boxed{sum \: of \: roots \: = \frac{1}{4} }$

To find :-

sum of roots .

Formula used :-

To find the sum of roots ,we applied

$\small \boxed{\bf{sum \: of \: roots \: = \frac{ - coefficient \: of \: x}{coefficient \: of \: {x}^{2} }}}$

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Step - by - step explanation :-

According to the question,

$\sqrt{3} x + 6 \sqrt{3x + 9 } = 0 \:$

We can write it,

$\sqrt{3} x = - 6 \sqrt{3x + 9}$

Now ,squaring on both sides ,

${( \sqrt{3} x)}^{2} = {( - 6 \sqrt{3x + 9}) }^{2} \\ \\ \implies \: 3 {x}^{2} = 36(3x + 9) \\ \\ \implies \: {x}^{2} = 12(3x + 9) \\ \\ \implies \: {x}^{2} = 36x + 144 \\ \\ \implies \: \boxed{ {x}^{2} - 36x - 144 = 0}$

Now ,

Applied the given formula ,

Then we get sum of roots ,

$\: sum \: of \: roots \: \implies \: \frac{ - ( - 36)}{144} \\ \\ \implies \: \frac{1}{4}$

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