Question

3x^2-2√5x-5=0 determine wheather to give quardartic wquation have real roots and if so find the roots
$3x { }^{2} - 2 \sqrt{5x } - 5 < = 0$

Answer 1

$3x^{2} - 2 \sqrt{5} x - 5 = 0 \\ a = 3 \\ b = - 2 \sqrt{5} \\ c = - 5 \\ {b}^{2} - 4ac = {( - 2 \sqrt{5}) }^{2} - 4(3)( - 5) \\ {b}^{2} - 4ac = 80 \\ x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} \\ x = \sqrt{5} \\ or \\ x = \frac{ - \sqrt{5} }{3}$