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If $\alpha, \beta$ are the zeroes of the polynomial $f(x)=5 x^{2}-7 x+1$, then $\frac{1}{\alpha}+\frac{1}{\beta}=?$
If $\alpha, \beta$ are the zeroes of the polynomial $f(x)=5 x^{2}-7 x+1$, then $\frac{1}{\alpha}+\frac{1}{\beta}=?$
CBSE | Class 10 | Excercise 2C | Maths | Polynomials | RS Aggarwal
If $\alpha, \beta$ are the zeroes of the polynomial $f(x)=5 x^{2}-7 x+1$, then $\frac{1}{\alpha}+\frac{1}{\beta}=?$

using the relationship between the zeroes of he quadratic polynomial.

=> Sum of zeroes $=\frac{-\text { (coef ficient of } x)}{\text { coefficient of } x^{2}}$ and Product of zeroes $=\frac{\text { constant term }}{\text { coefficient of } x^{2}}$

$\therefore \alpha+\beta=\frac{-(-7)}{5}$ and $\alpha \beta=\frac{1}{5}$

$\Rightarrow \alpha+\beta=\frac{7}{5}$ and $\alpha \beta=\frac{1}{5}$

Now, $\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha \beta}$

$=\frac{\frac{7}{5}}{\frac{1}{5}}$

$=7$

i

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