Question 1120457
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No; you can't tell what the equation is.<br>
Suppose the roots are p and q; then the equation is<br>
{{{(x-p)(x-q) = 0}}}
{{{x^2-px-qx+pq = 0}}}
{{{x^2-(p+q)x+pq = 0}}}<br>
Now suppose, for example, that you are told that the product of the roots is pq = 20.  Then you know the equation is<br>
{{{x^2-(p+q)x+20 = 0}}}<br>
where the product of p and q is 20.  But there are an infinite number of possibilities for that:<br>
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
....<br>
And those are only some of the possibilities where the roots are integers....