Question

Find a quadratic polynomial with zeroes 1 + square root of 2 and 1 - square root of 2​

Answer 1

Step-by-step explanation:

$1 + \sqrt{2 } \: \: and \: \: 1 - \sqrt{2} \: are \: \: the \: \: zeroes \\ \\ formula \: \: \: to \: \: \: find \: \: \: polynomial \: \: by \: \: zeroes = \\ \\ ax ^{2} - ( \alpha + \beta )x + \alpha \beta$

$\alpha \: and \: \: \beta \: \: are \: the \: \: zeroes$

$x ^{2} -( 1 + \sqrt{2} + 1 - \sqrt{2} ) + 1 + \sqrt{2} \times 1 - \sqrt{2}$

x²-x-1+2√2 is the answer

hope it helps you