Question

The quadratic equation with real coefficient whose one root is 5+underoot 5/2 is

Answer 1

Answer:

${x}^{2} - 5x + 10 = 0$

Step-by-step explanation:

$\alpha = \frac{5 + \sqrt{5} }{2} \\ \\ therefore \: \: \: \: \beta = \frac{5 - \sqrt{5} }{2} \\ \\ \\ \alpha + \beta = \frac{5 + \sqrt{5} }{2} + \frac{5 - \sqrt{5} }{2} = 10 \div 2 = 5 \\ \\ \\ \alpha \beta = ( \frac{5 + \sqrt{5} }{2} )( \frac{5 - \sqrt{5} }{2} ) = (25 - 5) \div 2 = \frac{20}{2} = 10 \\ \\ \\ equation \: is \: \: \: \: {x}^{2} - 5x + 10 = 0$