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**mathaddict** Q : If a, b and c $\displaystyle \in$ IR , with a is not 0 , and the roots of the equation $\displaystyle ax^2+bx+c=0$ are real , show that the roots of $\displaystyle a^2y^2-(b^2-2ac)y+c^2=0$ are also real .

If the roots of the quadratic equation $\displaystyle ax^2+bx+c=0$ are $\displaystyle \alpha$ and $\displaystyle \beta$ , state the value of $\displaystyle \alpha+\beta$ and $\displaystyle \alpha\beta$ in terms of a ,b and c . Hence , find the roots of the second equation in terms of $\displaystyle \alpha$ and $\displaystyle \beta$ .

I don understand this part only --- hence , find the roots of the second equation ( the last sentence )