Question

if one root of a quadratic polynomial is 3 minus root 8 then find the quadratic polynomial.

Answer 1

$if \: one \: root \: is \: 3 - \sqrt{8} \: then \: other \\ must \: be \: 3 + \sqrt{8} \: a s \: roots \: always \\ occur \: in \:conjugate \: pairs \: \\ quadratic \: equation = \\ {x }^{2} - (sum \: of \: roots)x \: + product \: \\ of \: roots = 0 \\ {x}^{2} - (3 - \sqrt{8 } + 3 + \sqrt{8} ) x + (3 - \\ \sqrt{8} )(3 + \sqrt{8} ) = 0 \\ {x}^{2} - 6x + 1 = 0$
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Answer 2

given root equals 3- √8 other will be 3+√8.
so the polynomial will be xsquare -6x +1