(B) For a cubic polynomial of the form $p(x) = ax^{3} + bx^{2} + cx + d$,the sum of the zeros $\alpha + \beta + \gamma$ is given by the formula $-\fra

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(B) For a cubic polynomial of the form $p(x) = ax^{3} + bx^{2} + cx + d$,the sum of the zeros $\alpha + \beta + \gamma$ is given by the formula $-\frac{b}{a}$.Given the polynomial $p(x) = x^{3} - 6x^{2} - 7x$,we identify the coefficients as $a = 1$,$b = -6$,$c = -7$,and $d = 0$.Substituting these values into the formula:$\alpha + \beta + \gamma = -\frac{-6}{1} = 6$.

Class 10 Mathematics Polynomials Relationship between Zeroes and Coefficients of a Polynomial

Medium

If $\alpha, \beta$ and $\gamma$ are the zeros of the cubic polynomial $p(x) = x^{3} - 6x^{2} - 7x$,then $\alpha + \beta + \gamma = \ldots$

A
$7$
B
$6$
C
$-6$
D
$-7$

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Relationship between Zeroes and Coefficients of a Polynomial

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If $\alpha, \beta$ and $\gamma$ are the zeros of the cubic polynomial $p(x) = x^{3} - 6x^{2} - 7x$,then $\alpha + \beta + \gamma = \ldots$

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