Question

please give reason for your answer ​

Answer 1

That's Easy

let the roots of the polynomial be

$\alpha . \: \beta and \: \gamma$

given that

$\alpha + \beta + \gamma = 2 \\ \alpha \beta + \beta \gamma + \gamma \alpha = - 7 \\ and \\ \alpha \beta \gamma = - 14$

therefore, the cubic polynomial equation is given by

${x}^{3} - ( \alpha + \beta + \gamma ) {x}^{2} + ( \alpha \beta + \beta \gamma + \gamma \alpha )x - \alpha \beta \gamma = 0$

so, required equation is

${x}^{3} - 2 {x}^{2} - 7x + 14 = 0$

hence, option (1) is correct.

Hope it helps （＾＿－）≡★