Question

If $\alpha$ and $\beta$ are the roots of the equation $3x^2-5x+2=0$, then find the values of $\frac{\alpha }{\beta }+\frac{\beta }{\alpha }$

• A. $\frac{13}{6}$
• B. $\frac{-13}{6}$
• C. $\frac{12}{6}$
• D. None of these

Answer 1

The correct option is A $\frac{13}{6}$

$\Rightarrow$ $\alpha$ and $\beta$ are the roots of the equation $3x^2-5x+2=0$.

$\Rightarrow$ $3x^2-5x+2=0$

$\Rightarrow$ $3x^2-3x-2x+2=0$

$\Rightarrow$ $3x(x-1)-2(x-1)=0$

$\Rightarrow$ $(x-1)(3x-2)=0$

$\Rightarrow$ $x=1$ and $x=\frac{2}{3}$

$\Rightarrow$ Since, $\alpha$ and $\beta$ are two roots then, $\alpha =1$ and $\beta =\frac{2}{3}$

$\Rightarrow$ $\frac{\alpha }{\beta }+\frac{\beta }{\alpha }$

$\Rightarrow$ $\frac{1}{\frac{2}{3}}+\frac{\frac{2}{3}}{1}$

$\Rightarrow$ $\frac{3}{2}+\frac{2}{3}$

$\Rightarrow$ $\frac{9+4}{2\times 3}$

$\Rightarrow$ $\frac{13}{6}$