Question:
If one root of the equation $3 x^{2}-10 x+3=0$ is $\frac{1}{3}$, then the other root is
(a) $\frac{-1}{3}$
(b) $\frac{1}{3}$
(c) $-3$
(d) 3
Solution:
(d) 3
Given:
$3 x^{2}-10 x+3=0$
One root of the equation is $\frac{1}{3}$.
Let the other root be $\alpha$.
We know that:
Product of the roots $=\frac{c}{a}$
$\Rightarrow \frac{1}{3} \times \alpha=\frac{3}{3}$
$\Rightarrow \alpha=3$