Question

Find a quadratic polynomial whose zeroes are (2-5√2) and (2+5√2)​

Answer 1

Answer:

x² - 4x - 46

Step-by-step explanation:

Answer 2

$Let \: \alpha = (2-5\sqrt{2}) \: and \\\beta = (2+5\sqrt{2})\: are \: zeroes \: of \: a \: Quadratic \\polynomial$

$i) Sum \: of \: the \: zeroes \\= \alpha + \beta \\= (2-5\sqrt{2}) + (2+5\sqrt{2}) \\= 2-5\sqrt{2}+ 2+5\sqrt{2}\\= 4 \: --(1)$

$ii) Product \: of \: the \: zeroes \\= \alpha \beta \\= (2-5\sqrt{2}) (2+5\sqrt{2}) \\= 2^{2} - (5\sqrt{2})^{2}\\= 4 - 50 \\= -46 \: --(2)$

$\underline { \blue { Form\: a \: Quadratic \: polynomial : }}$

$\blue { k[ x^{2} - (\alpha + \beta )x + \alpha \beta ) ] }$

$\red{ Required \: polynomial } \\= k(x^{2} - 4x -46)$

$We \: can \: put \: different \: values \: of \:k$

$When \: k = 1 , \: the \: Quadratic \: polynomial\\will \:be \: \green { x^{2} - 4x - 46 }$

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