Question

form a quadratic polynomial, one of whose zero is √5 and the product of the zeroes is -2√5

Answer 1

Given,
$\alpha + \beta = \sqrt{5 }\\ \alpha \beta = - 2 \sqrt{5} \\ p(x) = {x }^{2} - ( \alpha + \beta )x + \alpha \beta \\ \: \: \: \: \: \: \: \: \: = {x}^{2} - \sqrt{5} x - ( - 2 \sqrt{5} ) \\ \: \: \: \: \: \: \: \: \: = {x}^{2} - \sqrt{5} x + 2 \sqrt{5}$

Answer 2

$\huge\tt\colorbox{gold}{\green{❥answer࿐}}$

$\alpha + \beta = \sqrt{5 } \\ \alpha \beta = - 2 \sqrt{5} \\ p(x) = x ^{2} - ( \alpha + \beta )x + \alpha \beta \\ = x ^{2} - \sqrt{5} x - ( - 2 \sqrt{5} ) \\ = x ^{2} - \sqrt{5} x + 2 \sqrt{5}$