Question

If $\alpha$ and $\beta$ are zeros of the polynomial $2x^2-4x+5$, find the values of:
$\frac{1}{\alpha }+\frac{1}{\beta }$

• A. $-\frac{5}{4}$
• B. $-\frac{4}{5}$
• C. $\frac{5}{4}$
• D. $\frac{4}{5}$

Answer 1

The correct option is D $\frac{4}{5}$

$\left(\frac{1}{\alpha }\right)+\left(\frac{1}{\beta }\right)=\left(\frac{\beta +\alpha }{\alpha \beta }\right)=\left(\frac{\left(\frac{-b}{a}\right)}{\left(\frac{c}{a}\right)}\right)=\left(\frac{-b}{c}\right)=\left(\frac{-(-4)}{5}\right)=\left(\frac{4}{5}\right)$