Originally Posted by

**oxrigby** Q. Given that $\displaystyle \alpha$ and $\displaystyle \beta$ are roots of the equation $\displaystyle x^2+3x-6=0$, find a quadratic equation with integer coefficients whose roots are $\displaystyle \frac{2}{\alpha}$ and $\displaystyle \frac{2}{\beta}$

My working for this question basically gave me a wrong answer although i see it as perfectly ok. I basically used the quadratic formula and got$\displaystyle \frac{-3\pm\sqrt{33}}{2}$ and then i divided each one by 2 again giving the same answer but over 4. Then i just made brackets using the answer and got:$\displaystyle (x+\frac{3+\sqrt{33}}{4})(x+\frac{3-\sqrt{33}}{4})$ which expands to give $\displaystyle x^2+\frac{3x}{2}-\frac{3}{2}$ But the answer im supposed to get is $\displaystyle 3x^2-3x-2=0$ which i can't get. I f anyone could see whats wron with my method and show me how to get the right answer that'd be great unfortunatley my notes arent eith me atm thnx