Question

find a quadratic polynomial each with the given number as the number and the product of its zeros respectively 1.- 4, - 2​

Answer 1

$\alpha = 1 \\ \beta = - 4 \\ \gamma = - 2$

So,

$\alpha + \beta + \gamma = 1 - 4 - 2 = - 5$

$\alpha \beta + \beta \gamma + \gamma \alpha = - 4 + - 8 - 2 = - 14$

$\alpha \beta \gamma = - 8$

A cubic polynomial is given by,

${x}^{3} - ( \alpha + \beta + \gamma ) {x}^{2} + ( \alpha \beta + \beta \gamma + \gamma \alpha )x - ( \alpha \beta \gamma )$

Hence, the polynomial is

x³ + 5x² - 14x + 8