Question

Write a quadratic polynomial, whose sum of zeros is 2 and product is -8​

Answer 1

$if \: \alpha \: and \: \beta \: are \: the \: zeroes \: of \: the \: polynomial \\ then \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \alpha + \beta = 2 \: and \: \alpha \beta = - 8$

$p(x) = {x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ = {x}^{2} - 2x + ( - 8) \\ = {x}^{2} - 2x - 8$