Question

please solve stepp by step ​

Answer 1

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$Find \ the \ cubic \ polynomial \ whose \ zeroes </p><p> \\ are \ \alpha \ , \ \beta , \ \gamma \ such \ that \ \alpha + \beta + \gamma = 1 \ ,\\ \alpha \beta + \beta \gamma + \gamma \alpha = -10 , \ \alpha \beta \gamma = 8$

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$\boxed{\red{\bold{Given:}}}$

$\red{\implies}\alpha + \beta + \gamma = 1$

$\red{\implies}\alpha \beta + \beta \gamma + \gamma \alpha = -10$

$\red{\implies}\alpha \beta \gamma = 8$

$\boxed{\red{\bold{Polynomial :}}}$

$\purple{\implies}x^3 - (\alpha + \beta + \gamma)x^2 + (\alpha \beta + \beta \gamma + \gamma \alpha)x - \alpha \beta \gamma$

$\boxed{\red{\bold{Putting \ values:}}}$

$\green{\implies}x^3 - (1)x^2 + (-10)x - (8)$

$\green{\boxed{\implies{\boxed{x^3 - x^2 - 10x -8}}}}$

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