Question

Find a polynomial whose zeros are 2-√2 and3+√2

Answer 1

Step-by-step explanation:

$let \: \alpha \: and \: \beta be \: the \: zeros \: of \: required \: polynomial \\ therefore \\ \alpha = 2 - \sqrt{2} \\ \beta = 3 + \sqrt{2} \\ now \\ sum \: of \: zeros \\ \alpha + \beta = 2 - \sqrt{2} + 3 + \sqrt{2} = 5 \\ product \: of \: zeros \: \\ \alpha \beta = (2 - \sqrt{2} )(3 + \sqrt{2} ) \\ = 6 + 2 \sqrt{2} - 3 \sqrt{2} - 2 \\ = 4 - \sqrt{2} \\ required \: polynomial \: is \: \\ {x}^{2} - ( \alpha + \beta ) + \alpha \beta \\ = {x}^{2} - 5x +( 4 - \sqrt{2} )$