Question

If one of the roots of the equation $3x^2-10x+k=0$ is $\frac{1}{3}$ then find the other root and also the value of k.

Answer 1

The given equation is $3x^2-10x+k=0$

Let the two roots be $\alpha$ and $\beta$.

$\therefore \alpha +\beta =\frac{-(-10)}{3}=\frac{10}{3}$

Substituting $\alpha =\frac{1}{3}$ in (1) we get $\beta =3$

Also, $\alpha \beta =\frac{k}{3}$, $\to k=3$

Thus, the other root b = 3 and the value of k = 3