Question

find a quadratic polynomial whose zeroes are 5-3√2 and 5+3√2​

Answer 1

Answer:

$\bold\red{ † Answer † }$

$\small\bold{Given \: zeroes \: are :- }$

$\small\bold{5 + 3 \sqrt{2} \: and \: 5 - 3 \sqrt{2} }$

$\small\bold{Sum \: of \: the \: zeroes :}$

$\small\bold{5+3\sqrt{2} + 5 - 3\sqrt{2}}$

$\small\bold{ = 10}$

$\small\bold{Product \: of \: the \: zeroes :}$

$\small\bold{(5+3 \sqrt{2)} \:(5-3\sqrt{2)}}$

$\small\bold{5² - (3\sqrt{2})²}$

$\small\bold{ 25 - 18 }$

$\small\bold{ → 7}$

$\small\bold{ The \: required \: quadratic \: polynomial \: is }$

$\small\bold{x² - ( sum \: of \: the \: zeroes)x + product \: of \: the \: zeroes}$

$\small\bold{Answer → x² - 10x + 7}$

Answer 2

Answer:

Givenzeroesare:−

\small\bold{5 + 3 \sqrt{2} \: and \: 5 - 3 \sqrt{2} }5+3

2

and5−3

2

\small\bold{Sum \: of \: the \: zeroes :}Sumofthezeroes:

\small\bold{5+3\sqrt{2} + 5 - 3\sqrt{2}}5+3

2

+5−3

2

\small\bold{ = 10}=10

\small\bold{Product \: of \: the \: zeroes :}Productofthezeroes:

\small\bold{(5+3 \sqrt{2)} \:(5-3\sqrt{2)}}(5+3

2)

(5−3

2)

\small\bold{5² - (3\sqrt{2})²}5²−(3

2

)²

\small\bold{ 25 - 18 }25−18

\small\bold{ → 7}→7

\small\bold{ The \: required \: quadratic \: polynomial \: is }Therequiredquadraticpolynomialis

\small\bold{x² - ( sum \: of \: the \: zeroes)x + product \: of \: the \: zeroes}x²−(sumofthezeroes)x+productofthezeroes

\small\bold{Answer → x² - 10x + 7}Answer→x²−10x+7

Step-by-step explanation:

Mark me as brainliest answer