The product of zeros of a cubic polynomial p( | vedclass

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Question

(D) For a cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$,where $a 
eq 0$,let the zeros be $\alpha, \beta,$ and $\gamma$.According to the relationship

Vedclass · Accepted Answer

None of these

Vedclass · Answer

(D) For a cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$,where $a 
eq 0$,let the zeros be $\alpha, \beta,$ and $\gamma$.According to the relationship between zeros and coefficients:$1$. Sum of zeros: $\alpha + \beta + \gamma = -\frac{b}{a} = -\frac{	ext{coefficient of } x^2}{	ext{coefficient of } x^3}$$2$. Sum of product of zeros taken two at a time: $\alpha\beta + \beta\gamma + \gamma\alpha = \frac{c}{a} = \frac{	ext{coefficient of } x}{	ext{coefficient of } x^3}$$3$. Product of zeros: $\alpha\beta\gamma = -\frac{d}{a} = -\frac{	ext{constant term}}{	ext{coefficient of } x^3}$Since the given options do not include $-\frac{d}{a}$,the correct choice is $D$.

The product of zeros of a cubic polynomial $p(x) = ax^3 + bx^2 + cx + d$ is $\ldots \ldots \ldots$

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