If the zeros of the cubic polynomial p(x) = a | vedclass

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(C) For a cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$,the relationship between the zeros $\alpha, \beta, \gamma$ and the coefficients is given by V

Vedclass · Accepted Answer

$\frac{	ext{coefficient of } x}{	ext{coefficient of } x^3}$

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(C) For a cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$,the relationship between the zeros $\alpha, \beta, \gamma$ and the coefficients is given by Vieta's formulas:$1$. Sum of zeros: $\alpha + \beta + \gamma = -\frac{b}{a} = -\frac{	ext{coefficient of } x^2}{	ext{coefficient of } x^3}$$2$. Sum of the product of zeros taken two at a time: $\alpha\beta + \beta\gamma + \gamma\alpha = \frac{c}{a} = \frac{	ext{coefficient of } x}{	ext{coefficient of } x^3}$$3$. Product of zeros: $\alpha\beta\gamma = -\frac{d}{a} = -\frac{	ext{constant term}}{	ext{coefficient of } x^3}$Therefore,$\alpha\beta + \beta\gamma + \gamma\alpha = \frac{c}{a} = \frac{	ext{coefficient of } x}{	ext{coefficient of } x^3}$.

If the zeros of the cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$ $(a \neq 0, a, b, c, d \in R)$ are $\alpha, \beta,$ and $\gamma$,then $\alpha\beta + \beta\gamma + \gamma\alpha = \dots$

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