Question

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Answer 1

Equation:

==> √5x² + 9x + 4√5 = 0

On comparing,

a = √5 ; b = 9 ; c = 4√5

Quadratic Formula:

$= = > \: \: \frac{ - b \: \pm \: \sqrt{ {b}^{2} - 4ac } }{2a}$

Putting values of the required variables:

$= = > \: \: \frac{ - 9 \: \pm \: \sqrt{81 - 4 \times 4 \times 5} }{2 \sqrt{5} } \\ \\ = = > \: \: \frac{ - 9 \: \pm \: \sqrt{81 - 80} }{ 2\sqrt{5} } \times \frac{ \sqrt{5} }{ \sqrt{5} } \\ \\ = = > \: \: \frac{ \sqrt{5} ( - 9 \: \pm \: 1 )}{10}$

Case - (+ve)

$= = > \: \: x = \frac{ \sqrt{5}( - 9 + 1) }{10} \\ \\ = = > \: \: x = \frac{ \sqrt{5} \times - \cancel{8}}{ \cancel{10}} \\ \\ = = > \: \: x = \frac{ - 4 \sqrt{5} }{5}$

Case - (-ve)

$= = > \: \: x = \frac{ \sqrt{5}( - 9 - 1)}{10} \\ \\ = = > \: \: x = \frac{ \sqrt{5} \times - \cancel{10}}{ \cancel{10}} \\ \\ = = > \: \: x = - \sqrt{5}$