Question

Find the roots of the quadratic equation 3x^2+ 2√5x –5 = 0

Answer 1

Solution:-

$\bf{ \small \: Equation \implies3 {x}^{2} + 2 \sqrt{5}x - 5 }$

To find root of quadratic equation ,Use Quadratic formula

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

Comparing the equation with :-ax²+bx+c ,so

$\bf \: a = 3 \: \: or \: \: b = 2 \sqrt{5} \: \: or \: c = \: - 5$

So put the value on Quadratic formula

$x = \frac{ - 2 \sqrt{5} \pm \sqrt{(2 \sqrt{5 } ) {}^{2} - 4 \times 3 \times - 5 } }{2 \times 3}$

$x = \frac{ - 2 \sqrt{5} \pm \sqrt{4 \times 5 + 60} }{6}$

$x = \frac{ - 2 \sqrt{5} \pm \sqrt{80} }{6}$

$x = \frac{ - 2 \sqrt{5} + 4 \sqrt{5} }{6} \: \: and \: \: \: x = \frac{ - 2 \sqrt{5} - 4 \sqrt{5} }{6}$

$x = \frac{2 \sqrt{5} }{6} \: and \: x = \frac{ - 6 \sqrt{5} }{6}$

$x = \frac{ \not2 \sqrt{5} }{ \not6} \: and \: x = \frac{ - \not 6 \sqrt{5} }{ \not6}$

$\bf{ \boxed{Answer : \: root \: of\: x = \frac{\sqrt{5} }{3} \: \: and \: \: - \sqrt{5} }}$