Question

find the polynomial whose zeroes are 5 and -2

Answer 1

Alpha = 5

Beta = - 2

Sum of zeroes = 5 - 2= 3

Product of zeroes = 5 (-2) = - 10

Required polynomial is x^2 - (sum of zeroes)x + product of zeroes

= x^2 - 3x - 10

Answer 2

HEY HERE IS YOUR ANSWER



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General form of polynomial is if alpha and Beta are zeroes of the polynomial


$p(x) = {x}^{2} - (\alpha + \beta )x + \alpha \beta$

Therefore the polynomial is

$let \: \alpha = 5 \: and \: \beta = - 2 \\ \\ \alpha + \beta = 5 - 2 \\ = 3 \\ \\ \\ \alpha \beta = 5 \times - 2 \\ = - 10$
$p(x) = {x}^{2} - 3x - 10$

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