Question

If alpha beta and gamma are the zeros of the cubic polynomial Px=x³+x²-17x+15 then alpha beta +beta gamma +gama alpha =

Answer 1

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$Relation \: between \: the \: zeros \: of \: cubic \: polynomial : \\ \\ Sum \: of \: zeros : \\ ( \alpha + \beta + \gamma ) = \frac{ - b}{a} = \frac{ - coefficient \: of \: {x}^{2} }{coefficient \: of \: {x}^{3}} \\ \\ Sum \: of \: the \: product \: of \: zeros : \\ ( \alpha \beta + \beta \gamma + \gamma \alpha ) = \frac{c}{a} = \frac{ coefficient \: of \: {x}}{coefficient \: of \: {x}^{3}} \\ \\ Product \: of \: zeros: \\ ( \alpha \beta \gamma ) = \frac{ - d}{a} = \frac{constant}{coefficient \: of \: {x}^{3}} \\ \\ \\ now \: \\ P(x) = {x}^{3} + {x}^{2} - 17x + 15 \\ \\ \alpha \beta + \beta \gamma + \gamma \alpha = \frac{ - 1}{1} = - 1$

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