Question

$\alpha$ and $\beta$ are roots of equation:$2x^2-14x+7=0$. Find the value of $\frac{1}{\alpha }+\frac{1}{\beta }$.

Answer 1

A quadratic equations $a{x}^2+bx+c=0$ with roots $\alpha$ and $\beta$ can be written as $x^2-(\alpha +\beta )+\alpha \beta$.

Where $\alpha +\beta =\frac{-b}{a}$

$\alpha \beta =\frac{c}{a}$

The given equation can be rewritten in the same format as $x^2-7x+\frac{7}{2}$.

So, here $\alpha +\beta =7$ and $\alpha \beta =\frac{7}{2}$.

$\frac{1}{\alpha }+\frac{1}{\beta }=\frac{\alpha +\beta }{\alpha \beta }=\frac{7}{\frac{7}{2}}=2$.

So, the answer is $2$.