Question

Find a cubic polynomial whose zeros are 3 5 and minus 2

Answer 1

Hlo mate your solution

Answer 2

Hi mate your answer is....
Let as suppose,
$\alpha = 3 \\ \beta = 5 \\ \gamma = - 2$
Then,
$\alpha + \beta + \gamma = 3 + 5 - 2 = 6 \\ \alpha \beta + \beta \gamma + \gamma \alpha = 15 - 10 - 6 = - 1 \\ and \: \: \alpha \beta \gamma = 3 \times 5 \times ( - 2) = - 30$
Hence, the required polynomial is given by
$f(x) = x {}^{3} - ( \alpha + \beta + \gamma ) {x}^{2} + ( \alpha \beta + \beta \gamma + \gamma \alpha )x - \alpha \beta \gamma \\ = {x}^{3} - 6 {x}^{2} - x + 30$
I hope it will help you....
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