Write the quadratic equation such that the sum of its roots is and the product of its roots is I know that and
Hi, berserk! The easiest way to solve this problem is probably trial and error, but if you want the general solution with a more systematic approach:
Let the roots of our quadratic be . We have and . This gives us the system of linear equations:
Now, let be some arbitrary value . Then we have as our solution:
Now just pick a (nonzero) value for ! For example, with we have