The zeros of cubic polynomial p(x) = ax^3 + b | vedclass

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Question

(A) For a cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$,where $a, b, c, d$ are real numbers and $a 
eq 0$,let the zeros be $\alpha, \beta$,and $\gam

Vedclass · Accepted Answer

$\frac{c}{a}$

Vedclass · Answer

(A) For a cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$,where $a, b, c, d$ are real numbers and $a 
eq 0$,let the zeros be $\alpha, \beta$,and $\gamma$.According to the relationship between the coefficients and the zeros of a polynomial:$1$. The sum of the zeros: $\alpha + \beta + \gamma = -\frac{b}{a}$$2$. The sum of the product of the zeros taken two at a time: $\alpha\beta + \beta\gamma + \gamma\alpha = \frac{c}{a}$$3$. The product of the zeros: $\alpha\beta\gamma = -\frac{d}{a}$Therefore,the value of $\alpha\beta + \beta\gamma + \gamma\alpha$ is $\frac{c}{a}$.

The zeros of 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 $\alpha\beta + \beta\gamma + \gamma\alpha = \ldots$

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