Question

find the roots of the quadratic equation √2x^2+7x+5√2=0 using the quadratic formula.​

Answer 1

Solution :

By using quadratic formula

$\sf \implies x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ \bf here \\ \\ a = \sqrt{2} \\ \\ b = 7 \\ \\ c = 5 \sqrt{2}$

Substitute values in formula

$\sf \implies x = \frac{ - 7 \pm \sqrt{ {7}^{2} - 4 \times \sqrt{2} \times 5 \sqrt{2} } }{2 \times \sqrt{2} } \\ \\\sf \implies x = \frac{ - 7 \pm \sqrt{49- 40}}{2 \sqrt{2} } \\ \\ \sf \implies x = \frac{ - 7 \pm \sqrt{9}}{2 \sqrt{2}} \\ \\\sf \implies x = \frac{ - 7 \pm9}{2 \sqrt{2}}$

$\bf Taking \: + ve \: sign \\ \\ x = \frac{ - 7 + 9}{2 \sqrt{2}} \\ \\\sf \implies x = \frac{2}{2 \sqrt{2}} \\ \\\sf \implies x = \frac{1}{ \sqrt{2} } \\ \\ \implies \sf x= \frac{ \sqrt{2} }{2}$

$\bf Taking \: - ve \: sign \\ \\\sf \implies x = \frac{ - 7 - 9}{2 \sqrt{2}} \\ \\\sf \implies x = \frac{ - 16}{2 \sqrt{2}} \\ \\ \sf \implies x = \frac{ - 8}{ \sqrt{2} } \\ \\\sf \implies x = \frac{ - 8\sqrt{2} }{2}$