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

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(B) 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 of the polynomial be $\alpha

Vedclass · Accepted Answer

$-\frac{	ext{coefficient of } x^2}{	ext{coefficient of } x^3}$

Vedclass · Answer

(B) 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 of the polynomial be $\alpha, \beta,$ and $\gamma$.According to the relationship between zeros and coefficients of a cubic polynomial:$1$. The sum of zeros: $\alpha + \beta + \gamma = -\frac{b}{a}$.$2$. The sum of the product of zeros taken two at a time: $\alpha\beta + \beta\gamma + \gamma\alpha = \frac{c}{a}$.$3$. The product of zeros: $\alpha\beta\gamma = -\frac{d}{a}$.Here,$b$ is the coefficient of $x^2$ and $a$ is the coefficient of $x^3$.Therefore,$\alpha + \beta + \gamma = -\frac{	ext{coefficient of } x^2}{	ext{coefficient of } x^3}$.

Part $I$	Part $II$
$1.$ The graph of $p(x)=x^{2}-5x+6$	$a.$ Intersects the $X$-axis at one point.
$2.$ The graph of $p(x)=x^{2}-10x+25$	$b.$ Intersects the $X$-axis at zero points.
$3.$ The graph of $p(x)=x^{3}-4x$	$c.$ Intersects the $X$-axis at two points.
$4.$ The graph of $p(x)=x^{2}+4x+5$	$d.$ Intersects the $X$-axis at three points.

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 $\alpha + \beta + \gamma = \ldots$

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