Question

If one root of the equation $3x^2-10x+3=0\mathrm{is}\frac{1}{3},$ then the other root is
(a) $\frac{-1}{3}$
(b) $\frac{1}{3}$
(c) −3
(d) 3

Answer 1

(d) 3
$$\begin{gathered} \text{Given:} \\ \text{3}{x}^2-10x+3=0 \\ \mathrm{One}\mathrm{root}\mathrm{of}\mathrm{the}\mathrm{equation}\mathrm{is}\frac{1}{3}. \\ \text{Let the other root be}\alpha . \\ \mathrm{We}\mathrm{know}\mathrm{that}: \\ \text{Product of the roots =}\frac{c}{a} \\ \Rightarrow \frac{1}{3}\times \alpha =\frac{3}{3} \\ \Rightarrow \alpha =3 \end{gathered}$$