If α and β are the zeros of the quadratic polynomial p(y)

Since $\alpha$ and $\beta$ are the zeros of the quadratic polynomial $p(y)=5 y^{2}-7 y+1$

$\alpha+\beta=\frac{-\text { Coefficient of } x}{\text { Coefficient of } x^{2}}$

$=-\frac{(-7)}{5}$

$=\frac{7}{5}$

$\alpha \beta=\frac{\text { Constant term }}{\text { Coefficient of } x^{2}}$

$=\frac{1}{5}$

We have, $\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha \beta}$

By substituting $\alpha+\beta=\frac{7}{5}$ and $\alpha \beta=\frac{1}{5}$ we get,

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

$\frac{1}{\alpha}+\frac{1}{\beta}=7$

Hence, the value of $\frac{1}{\alpha}+\frac{1}{\beta}$ is 7 .