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Q.
If $\alpha$ and $\beta$ are the roots of the equation $2 x^2-7 x+12=0$, then $\frac{1}{\alpha}+\frac{1}{\beta}=$___
Quadratic Equations
Solution:
Given: $\alpha$ and $\beta$ are the roots of the equation.
$2 x^2-7 x+12=0 $
$ \Rightarrow \alpha+\beta=\frac{-b}{a}=\frac{7}{2} $
$ \alpha \beta=\frac{c}{a}=\frac{12}{2}=6 $
$ \frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha \beta}=\frac{\left(\frac{7}{2}\right)}{6}=\frac{7}{12}=0.583$