Question

A polynomial whose zeroes are

$5 + \sqrt{2} and \: 5 - \sqrt{2 \: } is$
(direct answer is enough)​

Answer 1

Answer:

${x}^{2} - 10x + 23 = 0$

Step-by-step explanation:

Sum of roots =

$5 + \sqrt{2} + 5 - \sqrt{2} = 10$

Product of roots =

$(5 + \sqrt{2} )(5 - \sqrt{2} ) = 25 - 2 = 23$

Equation

${x}^{2} - (sum)x + (product) = 0 \\ {x}^{2} - 10x + 23 = 0$