For the zeros alpha and beta of the polynomia | vedclass

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(A) Given the polynomial $p(x) = ax^2 + bx + c$ with zeros $\alpha$ and $\beta$.From the relationship between zeros and coefficients:Sum of zeros: $\a

Vedclass · Accepted Answer

$-\frac{b}{c}$

Vedclass · Answer

(A) Given the polynomial $p(x) = ax^2 + bx + c$ with zeros $\alpha$ and $\beta$.From the relationship between zeros and coefficients:Sum of zeros: $\alpha + \beta = -\frac{b}{a}$Product of zeros: $\alpha \cdot \beta = \frac{c}{a}$We need to find $\frac{1}{\alpha} + \frac{1}{\beta}$.Taking the common denominator: $\frac{1}{\alpha} + \frac{1}{\beta} = \frac{\alpha + \beta}{\alpha \cdot \beta}$.Substituting the values: $\frac{-\frac{b}{a}}{\frac{c}{a}} = -\frac{b}{a} \cdot \frac{a}{c} = -\frac{b}{c}$.Therefore,the correct option is $A$.

For the zeros $\alpha$ and $\beta$ of the polynomial $p(x) = ax^2 + bx + c$,what is the value of $\frac{1}{\alpha} + \frac{1}{\beta}$?

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