Question

Find a quadratic polynomial whose zeroes are 2+√5 and -√5​

Answer 1

Step-by-step explanation:

quadratic equation :

x² - (sum of zeroes) x + (product of zeroes)

zeroes ==

$\alpha = 2 + \sqrt{5}$

$\beta = - \sqrt{5}$

therefore,

${x}^{2} - (2 + \sqrt{5} + ( - \sqrt{5} ))x + ((2 + \sqrt{5}) \times ( - \sqrt{5} ))$

${x}^{2} - 2x + ( - 2 \sqrt{5} - 5)$

${x}^{2} - 2x - 2 \sqrt{5} - 5$