Question

find the quadratic polynomial with the sum, of the product of its zeroes taken two at a time and the product of its zeroes as 2,-7 respectively​

Answer 1

Answer:

x²-2x+(-7)

=x²-2x-7

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Answer 2

$Let \: \alpha \:and \: \beta \: are \: two$

$zeroes \:of \: a \: Quadratic \: polynomial.$

$Given \: \alpha + \beta = 2 \:and \: \alpha \beta = -7$

$The \: Quadratic \: polynomial \: is :$

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

$where \: k \: is \: a \: constant$

$= k[ x^{2} -2x + (-7) ]$

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

$When \: k = 1 ,$

$\green { The \: Quadratic \: polynomial \:will }$

$\green {be \: x^{2} - 2x - 7}$

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