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Question

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

Vedclass · Accepted Answer

$-\frac{d}{a}$

Vedclass · Answer

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

If $\alpha, \beta$,and $\gamma$ are the zeros of the cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$ where $a \neq 0$,then the product of its zeros $(\alpha \beta \gamma)$ is:

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