Question

If $\alpha$ and $\beta$ are the roots of the equation $3x^2+x-10=0$, then the value of $\frac{1}{\alpha }+\frac{1}{\beta }$ is

• A. $10$
• B. $-\frac{1}{10}$
• C. $\frac{1}{10}$
• D. $\frac{1}{3}$

Answer 1

The correct option is C $\frac{1}{10}$

$3x^2+x-10=0$

$\alpha ,B$ are roots

$\Rightarrow \alpha +B=\frac{-b}{a}=\frac{-1}{3}$

$\alpha \beta =\frac{c}{a}\frac{-10}{3}$

$\frac{1}{\alpha }+\frac{1}{\beta }=\frac{(\alpha +\beta )}{\left(\alpha \beta \right)}=\frac{(-1/3)}{-\left(10\right)/3}\Rightarrow \frac{1}{10}$

$\therefore \frac{1}{\alpha }+\frac{1}{\beta }=\frac{1}{10}$