The roots of the quadratic equation are and . Find two distinct quadratic equations whose roots are and .

My steps:

Sum of roots,

Product of roots,

Sum of new roots,

Product of new roots,

But it turns out I'm partially correct, because while there is a before , there is not supposed to be a before .

After staring at it for a couple minutes I'm guessing that since the original equation has a positive c/a, hence my new product of roots must be positive too. Am I right?