SOLUTION: Suppose the product of the roots of a quadratic equation is given, do you think you can determine the equation? Justify your answer.

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Question 1120457: Suppose the product of the roots of a quadratic equation is given, do you think you can determine the equation? Justify your answer.
Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Not necessarily.
If the roots are not real, such as 1+i and 1-i, whose product is 2, one could determine AN equation, like x^2-2x+2, but 2 and 1 could be roots as well, and that equation is x^2-3x+2

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


No; you can't tell what the equation is.

Suppose the roots are p and q; then the equation is

%28x-p%29%28x-q%29+=+0
x%5E2-px-qx%2Bpq+=+0
x%5E2-%28p%2Bq%29x%2Bpq+=+0

Now suppose, for example, that you are told that the product of the roots is pq = 20. Then you know the equation is

x%5E2-%28p%2Bq%29x%2B20+=+0

where the product of p and q is 20. But there are an infinite number of possibilities for that:

p, q = 20 and 1: x^2-21x+20 = 0
p, q = 10 and 2: x^2-12x+20 = 0
p, q = 5 and 4: x^2-9x+20 = 0
p, q = -5 and -4: x^2+9x+20 = 0
....

And those are only some of the possibilities where the roots are integers....