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If x²-3x+c=(x-p)(x-q)=x²=x-(p+q)x+pq.

So p+q=3, that is, q=3-p.

(p,q)={(1,2), (4,-1), (5,-2), (6,-3), (7,-4), ...};

c=pq={2,-4, -10, -18, -28, ...}

In general then c=p(3-p) or c=3p-p². (Also when p=0, q=3, c=0.)

by Top Rated User (894k points)

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