find a cubic polynomial with the sum ,sum of the product of its zero taken two at a time and the product of its zeroes are 3,-8,-12 respectively. Created by hritiksingh1. Math

Let be the roots of the cubic polynomial.Then, Therefore,

find a cubic polynomial with the sum ,sum of the product of its zero taken two a...

Hades09 Let
$\alpha \: \: \beta \: \: \gamma$
be the roots of the cubic polynomial.
Then,
$\alpha + \beta + \gamma = 3$
$\alpha \beta + \beta \gamma + \gamma \alpha = - 8$
$\alpha \beta \gamma = - 12$
Therefore,
${x}^{3} - ( \alpha + \beta + \gamma) {x}^{2} + ( \alpha \beta + \beta \gamma + \gamma \alpha ) x - ( \alpha \beta \gamma ) = 0$
${x}^{3} - 3 {x}^{2} - 8x - 12 = 0$

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