Question

If $\alpha$ and $\beta$ are the zeroes of the polynomial. $x^2+x-2,$ then find the value of $\frac{\alpha }{\beta }+\frac{\beta }{\alpha }$ .

Answer 1

Consider the given polynomial.

$\Rightarrow x^2+x-2$

Since, $\alpha$ and $\beta$ are the zeroes of the polynomial.

$\alpha +\beta =-1$

$\alpha \beta =-2$

Since,

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

$=\frac{{\alpha }^2+{\beta }^2}{\alpha \beta }$

$=\frac{(\alpha +\beta {)}^2-2\alpha \beta }{\alpha \beta }$

Therefore,

$=\frac{(-1{)}^2-2\times -2}{-2}$

$=\frac{1+4}{-2}$

$=\frac{-5}{2}$

Hence, this is the answer.