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

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(C) Given the cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$,the relationships between the zeros $\alpha, \beta, \gamma$ and the coefficients are:$\al

Vedclass · Accepted Answer

$\frac{bd}{a^2}$

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(C) Given the cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$,the relationships between the zeros $\alpha, \beta, \gamma$ and the coefficients are:$\alpha + \beta + \gamma = -\frac{b}{a}$$\alpha \beta + \beta \gamma + \gamma \alpha = \frac{c}{a}$$\alpha \beta \gamma = -\frac{d}{a}$We need to evaluate the expression: $\alpha^2 \beta \gamma + \alpha \beta^2 \gamma + \alpha \beta \gamma^2$Factor out the common term $\alpha \beta \gamma$:$= \alpha \beta \gamma (\alpha + \beta + \gamma)$Substitute the known values:$= (-\frac{d}{a}) 	imes (-\frac{b}{a})$$= \frac{bd}{a^2}$

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 $\alpha^2 \beta \gamma + \alpha \beta^2 \gamma + \alpha \beta \gamma^2 = \dots$

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