Question

olve the followjng quadratic equation 2x²–√3x+1=0​

Answer 1

Step-by-step explanation:

$2 {x}^{2} - \sqrt{3} x + 1 = 0 \\ match \: into \: \\ a {x}^{2} + bx + c = 0 \\ a = 2 \: \: b = - \sqrt{3} \: \: c = 1 \\ roots \: = \frac{ - b \frac{ + }{ } \sqrt{ {b}^{2} - 4ac } }{2a} \\ = \frac{ - ( - \sqrt{3}) \frac{ + }{} \sqrt{ {( - \sqrt{3} ) }^{2} - 4(2)(1) } }{2(2)} \\ = \frac{ \sqrt{3} \frac{ + }{} \sqrt{3 - 8} }{4} \\ = \frac{ \sqrt{3} + \sqrt{5} }{4} \: \: \: \: \: = \frac{ \sqrt{3} - \sqrt{5} }{4} \\ \\ roots \: are \: \\ \frac{ \sqrt{3} + \sqrt{5} }{4} \: \: \: \: \frac{ \sqrt{3} - \sqrt{5} }{4}$