Question

Write a quadratic polynomial,the sum and product of whose zeroes are 3 and -2

Answer 1

$let \: \alpha \: and \: \beta \: be \: the \: roots \: of \: the \: \\ desired \: equation$

so,

it's given that;

$\alpha + \beta = 3 \\ \: \: \: \: \: \: \alpha \beta = - 2 \\ \\ now \\ we \: know \: that \\ \\ p(x) = {x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ p(x) = {x}^{2} - 3x + ( - 2) \\ p(x) = {x}^{2} - 3x - 2$

Hence, the desired polynomial is x² - 3x - 2.