Question

find a cubic polynomial whose zeros are 3,4,and -2​

Answer 1

Answer:

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$\alpha = 3 \\ \beta = 4 \\ \gamma = - 2 \\ \\ \alpha + \beta + \gamma = \frac{ - b}{a} = 5 \\ \alpha \beta + \beta \gamma + \gamma \alpha = \frac{c}{a} = - 2 \\ \alpha \beta \gamma = \frac{ - d}{a} = - 24 \\ \\ x {}^{3} - ( \alpha + \beta + \gamma ) {x}^{2} + ( \alpha \beta + \beta \gamma + \gamma \alpha )x - \alpha \beta \gamma \\ x {}^{3} - {5x }^{2} - 2x + 24 \: is \: the \: required \: quadratic \: polynomial$