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  4. If the roots of the quadratic equation are α and β, then its equation can be written as (x-α)(x-β)=0 i.e. x2-x(α+β)+α β=0 (1/α)+(1/β)

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Q. If the roots of the quadratic equation are $\alpha$ and $\beta$, then its equation can be written as $(x-\alpha)(x-\beta)=0$ i.e. $x^2-x(\alpha+\beta)+\alpha \beta=0$
$\frac{1}{\alpha}+\frac{1}{\beta}$

Quadratic Equations

Solution:

Given quadratic equation is $x^2-10 x+25$
$\alpha+\beta=10 $
$ \alpha \beta=25$
Now, $\frac{1}{\alpha}+\frac{1}{\beta}=\left(\frac{\alpha+\beta}{\alpha \beta}\right)$
$\frac{\alpha+\beta}{\alpha \beta}=\frac{10}{25}=\frac{2}{5}$