Question

Example 11 Solve √5x² + x + √5 = 0​

Answer 1

Answer:

$\sqrt{5} {x}^{2} + x + \sqrt{5} = 0 \\ a = \sqrt{5} \: \: \: \: \: \: \: \: b = 1 \: \: \: \: \: \: \: \: c = \sqrt{5} \\ then \: \\ distriminant(d) = \sqrt{ {b}^{2} - 4ac } \\ = \sqrt{ {1}^{2} - 4 \times \sqrt{5} \times \sqrt{5} } \\ = \sqrt{1 - 20} = \sqrt{ - 19} \\ so \: it \: has \: no \: real \: roots \\ x1 =( - 1 + \sqrt{ - 19} ) \div 2 \sqrt{5} \\ and \\ x2 = ( - 1 - \sqrt{ - 19} ) \div 2 \sqrt{5}$