Question

find a cubic polynomial whose zero are 5,6and -4​

Answer 1

the zeros are 5, 6, -4

$\alpha = 5 \: \: \beta = 6 \: \: \: \: \gamma = - 4 \\ \alpha + \beta + \gamma = 5 + 6 - 4 = 7 \\ \alpha \beta + \beta \gamma + \alpha \gamma = 30 - 24 - 20 = - 14 \\ \alpha \beta \gamma = 5 \times 6 \times - 4 = - 120\\ {x}^{3} + ( \alpha \beta \gamma ) {x}^{2} + ( \alpha \beta + \beta \gamma + \alpha \gamma )x + \alpha \beta \gamma \\ {x}^{3} + 7 {x}^{2} - 14x - 120$